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 \( |a \times b|\).