Jamieson, Fausset and Brown on Daniel 1:21

21. Daniel continued ... unto ... first year of Cyrus--(2Ch 36:22; Ezr 1:1). Not that he did not continue beyond that year, but the expression is designed to mark the fact that he who was one of the first captives taken to Babylon, lived to see the end of the captivity. See my Introduction, "Significance of the Babylonian Captivity." In Da 10:1 he is mentioned as living "in the third year of Cyrus." See Margin Note, on the use of "till" (Psa 110:1, 112:8).