I have a question which is:
If $f$ is an integrable function on $[a,b]$ and $\int_{a}^{b}{f(x)\,dx}>1$, then there exists a point $c\in(a,b)$ such that $\int_{a}^{c}{f(x)\,dx}=1$.
This seems true to me intuitively. But I can't seem to prove or disprove it. Can someone help me? Thanks :)