Solving the integrals equation

Here is a little refresher of your calculus knowledge ---a step-by-step presentation on how to solve the integrals equation using Pierre de Fermat method.

But this is only the first part of the presentation. Read the second article here.
At the end of the article the author Chris Sangwin from the University of Birmingham has a little test for you:

If this article has inspired you to do some calculus, here is a problem for you: