PART A:How does the author use references to the personal histories of Prospero and Caliban to advance the plot

He uses the histories of both characters, so that readers know why Prospero is dealing the Caliban in such a way.

By providing two contrasting points of view about the history between Prospero and Caliban, the author creates tension and establishes a central conflict.

(This may not be correct, but given the previous answer, this is the closest one on commonlit.)

Part B: which detail from the texts supports the answer to part A?

What detail from the text support your answer to question 6

Prospero claims to have provided Caliban comfortable lodging while Caliban claims to be imprisoned.