Does f(x) f(x) not matter?

Calculus Level 4

A strictly increasing and continuous function f(x)f(x) intersects with its inverse f1(x)f^{-1}(x) at points x=ax=a and x=bx=b, where aa and bb are integers.

If ab[f(x)+f1(x)]dx=17 \displaystyle \int_a^b[f(x) + f^{-1}(x)] \, dx = 17 , find a×b |a \times b|.

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