We are told that $g(x)$ is Riemann integrable on $[a,b]$ and $\int_{a}^{b}g(x)=0$ also that $0≤f(x)≤g(x)$ and asked to prove $f(x)$ is Riemann integrable and that $\int_{a}^{b}f(x)=0$.
Intuitively $g$ must be a special kind of function, like $0$, or $0$ with 'spikes' or perhaps if not, then $a=b$.
But how to start a proof? Direction appreciated.