Riemann Integrable -- Is this true?

Question

I have a sequence of functions $f_n$ (on a compact interval) which uniformly converge to $f$, and I know $f$ is Riemann Integrable. Is it true that $f_n$ must also be Riemann Integrable?

Answer 1

No. Let $f$ be your favorite bounded, non Riemann integrable function and $f_n=f/n$.