The question is as stated in the title:
If $f$ is continuous almost everywhere on $[a,b]$, is it true that $f$ is Riemann integrable on $[a,b]$?
The natural thought is Lebesgue's criterion, which states that "A bounded function on a compact interval [a, b] is Riemann integrable if and only if it is continuous almost everywhere".
Hence, if we remove the condition "bounded", the statement becomes false right? I would see that the upper sum goes to infinity.
What would be a good concrete counterexample?