Could someone give me a hand on this problem? I want to show that a bounded function $\displaystyle f: [a,b] \rightarrow R$ having a convergent sequence of discontinuous points is Riemann integrable.

I was able to show that that a function bounded function having finitely many discontinuous points is Riemann integrable.

I think I need to come up with a partition P such that $\displaystyle U(P,f)-L(P,f) < \epsilon$ for this problem.