




If you can integrate f(x), you can integrate its inverse function as well.
You have:
A_{1}_{ }+ _{ }A_{2}_{ }= A_{3 } A_{4}_{ }
This can be seen to hold from the pictures, in which f(x) must be an increasing or decreasing function of x. (the inverse is not well defined unless f is one or the other.). Suppose f is increasing.