Suppose that two functions $|f|, f^2 $ are Riemann integrable function on $[a, b] \in \mathbb R$.
I want to show that
$$ \int_{a}^{b} |f| = 0 \iff \int_{a}^{b} f^2 = 0 $$
Remember that we don't know whether the function $ f $ is continuous or not.
If $ f $ is continuous, it is very easy. But i want to prove that $ f $ is not continuous.
I have been tried a lot of methods, but i can't prove it. Plz help