I am wondering of a proof strategy to show. That a sequence of Riemann integrable functions which converges point wise to a function may not actually uniformly converge to it. If it makes the argument simpler i also know that the function $f$ the sequence of functions are converging point wise to, is not Riemann integrable. Although on a second thought is it possible to build such an argument without the knowledge of $f$ being non-Riemann integrable ?
Any help would be much appreciated.