Primitive function of inverse function/Formula via substitution and integration by parts/Exercise

Let

$f\colon [a,b]\longrightarrow [c,d]$

be a bijective, continuous differentiable function. Prove the formula for the antiderivative of the inverse function by the integral

$\int _{a}^{b}f^{-1}(y)dy$

using the substitution ${}y=f(x)$ and then integration by parts.

Create a solution