If $f:[a,b]\to\mathbb{R}$ is Riemann-integrable then it is continuous at a point in $[a,b]$.
First of all, I already know the Lebesgue's criterion for Riemann-integrability. So such a function will be continuous almost everywhere. But could we prove a weaker result (the above one) without using the Lebesgue's criterion, which requires a difficult proof?
What do you think?
