Answer:
Daniel read the books and letters of his people [some of which Jeremiah wrote through Baruch - Jer.36:4] that were confiscated and taken to Babylon in the captivity of the Jews:
"Now these are the words of the letter that Jeremiah the prophet sent from Jerusalem unto the residue of the elders which were carried away captives, and to the priests, and to the prophets, and to all the people whom Nebuchadnezzar had carried away captive from Jerusalem to Babylon... That after seventy years be accomplished at Babylon I will visit you, and perform My Good Word toward you, in causing you to return to this place." (Jer.29:1 & 10)
"...I Daniel understood by books the number of the years, whereof the Word of the Lord came to Jeremiah the prophet, that He would accomplish seventy years in the desolations of Jerusalem." (Dan.9:2)