Can someone help me do this problem?
Let $f$ be s Riemann integrable function on $[a,b]$ not necessarily continuous.Prove that there exists a sequence $\{g_n\}_{n\in \mathbb{N}}$of continuous functions on $[a,b]$ such that $$\lim_{n\to \infty} \int_a^b |g_n(x)-f(x)|\ dx=0$$