Volterra in 1881, proved that there exists a function, [math]F(x) [/math]whose derivative exists and is bounded for all [math]x\in [a,b][/math], however, the derivative [math]F'(x)[/math] is not Riemann integrable. Actually the derivative is discontinuous on a dense set with positive outer content.
It is a very complex function and it is not easy to make a representation. Here there is an approach.
