Assume that $f: [a, b] \rightarrow [a,b]$ is continuously differentiable bijection and that $f(a) = a$, $f(b) = b$.
$$\int_a^b g(x) \, dx + \int_a^b f(x) \, dx = b^2-a^2$$
where $g:[a, b] \rightarrow [a, b]$ is the inverse function of $f$
With this one I have no idea where to start. What should we do with the information about $f$ being bijective and $g$ being the inverse of $f$?