$f(x)$ is continuous on $[0,\pi]$.Prove that the following limit is $\frac{2}{\pi}\int_{0}^{\pi}f(x)$
Computing $\lim_{n \rightarrow\infty} \int_{a}^{b}\left ( f(x)\left | \sin(nx) \right | \right )$ with $f$ continuous on $[a,b]$