Romans 5:12-21: "12 Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned - 13 for sin indeed was in the world before the law was given, but sin is not counted where there is no law. 14 Yet death reigned from Adam to Moses, even over those whose sinning was not like the transgression of Adam, who was a type of the one who was to come.
"15 But the free gift is not like the trespass. For if many died through one man's trespass, much more have the grace of God and the free gift by the grace of that one man Jesus Christ abounded for many. 16 And the free gift is not like the result of that one man's sin. For the judgement following one trespass brought condemnation, but the free gift following many trespasses brought justification. 17 For if, because of one man's trespass, death reigned through that one man, much more will those who receive the abundance of grace and the free gift of righteousness reign in life through the one man Jesus Christ.
"18 Therefore, as one trespass led to condemnation for all men, so one act of righteousness leads to justification and life for all men. 19 For as by the one man's disobedience the many were made sinners, so by the one man's obedience the many will be made righteous. 20 Now the law came in to increase the trespass, but where sin increased, grace abounded all the more, 21 so that, as sin reigned in death, grace also might reign through righteousness leading to eternal life through Jesus Christ our Lord."
[To be consistent, I used the ESV translation, but I think the redundant "free gift" is a poor rendering. For what it's worth, here's the Greek interlinear.]
1 Corinthians 15:21-22: "21 For as by a man came death, by a man has come also the resurrection of the dead. 22 For as in Adam all die, so also in Christ shall all be made alive."
1 Corinthians 15:45: "Thus it is written, 'The first man Adam became a living being'; the last Adam became a life-giving spirit."
Romans 3:12: "'All have turned aside; together they have become worthless; no one does good, not even one.'"
Genesis 3:1-19: "1 Now the serpent was more crafty than any other beast of the field that the LORD God had made.
"He said to the woman, 'Did God actually say, "You shall not eat of any tree in the garden"?' 2 And the woman said to the serpent, 'We may eat of the fruit of the trees in the garden, 3 but God said, "You shall not eat of the fruit of the tree that is in the midst of the garden, neither shall you touch it, lest you die."' 4 But the serpent said to the woman, 'You will not surely die. 5 For God knows that when you eat of it your eyes will be opened, and you will be like God, knowing good and evil.' 6 So when the woman saw that the tree was good for food, and that it was a delight to the eyes, and that the tree was to be desired to make one wise, she took of its fruit and ate, and she also gave some to her husband who was with her, and he ate. 7 Then the eyes of both were opened, and they knew that they were naked. And they sewed fig leaves together and made themselves loincloths.
"8 And they heard the sound of the LORD God walking in the garden in the cool of the day, and the man and his wife hid themselves from the presence of the LORD God among the trees of the garden. 9 But the LORD God called to the man and said to him, 'Where are you?' 10 And he said, 'I heard the sound of you in the garden, and I was afraid, because I was naked, and I hid myself.' 11 He said, 'Who told you that you were naked? Have you eaten of the tree of which I commanded you not to eat?' 12 The man said, 'The woman whom you gave to be with me, she gave me fruit of the tree, and I ate.' 13 Then the LORD God said to the woman, 'What is this that you have done?' The woman said, 'The serpent deceived me, and I ate.'
"14 The LORD God said to the serpent, 'Because you have done this, cursed are you above all livestock and above all beats of the field; on your belly you shall go, and dust you shall eat all the days of your life. 15 I will put enmity between you and the woman, and between your offspring and her offspring; he shall bruise your head, and you shall bruise his heel.'
"16 To the woman he said, 'I will surely multiply your pain in childbearing; in pain you shall bring forth children. Your desire shall be for your husband, and he shall rule over you.'
"17 And to Adam he said, 'Because you have listened to the voice of your wife and have eaten of the tree of which I commanded you, "You shall not eat of it," cursed is the ground because of you; in pain you shall eat of it all the days of your life; 18 thorns and thistles it shall bring forth for you; and you shall eat the plants of the field. 19 By the sweat of your face you shall eat bread, till you return to the ground, for out of it you were taken; for you are dust, and to dust you shall return.'"
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The text is public domain:
All mankind fell in Adam's fall;One common sin infects us all.From one to all the curse descends,And over all God's wrath impends.
Through all our pow'rs corruption creepsAnd us in dreadful bondage keeps;In guilt we draw our infant breathAnd reap its fruits of woe and death.
From hearts depraved, to evil prone,Flow thoughts and deeds of sin alone;God's image lost, the darkened soulSeeks not nor finds its heav'nly goal.
But Christ, the second Adam, cameTo bear our sin and woe and shame,To be our life, our light, our way,Our only hope, our only stay.
As by one man all mankind fellAnd, born in sin, was doomed to hell,So by one Man, who took our place,We all were justified by grace.
We thank You, Christ; new life is ours,New light, new hope, new strength, new pow'rs.This grace our ev'ry way attendUntil we reach our journey's end.
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The first two lines of the hymn ("All mankind fell in Adam's fall; / One common sin infects us all.") come from the first part of the text from Romans 5. The second verse also comes from Romans 5 but seems to incorporate parts of 1 Corinthians 15:21-22 too. The third verse seems to draw from Romans 3:12. Of course, the text from Genesis 3 is the background for all of this.
The second half of the hymn comes primarily from Romans 5, although parts of the passages from 1 Corinthians 15 are also present in the last verse, specifically: "new life is ours."
