Does $f(x)$ not matter?

Calculus Level 4

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

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

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

Does $f(x)$ not matter?