I am working through a Real Analysis textbook and found the following exercise.
Let $f\,:\,[a,b]\rightarrow\mathbb R$ be Riemann integrable and nonnegative. Suppose $$\int_a^bf(x)\,dx=0.$$ Find $f$.
I know that this should come out to be that $f(x)=0$ logically, but how could I show this with some rigor?