Is it true that a function is Riemann integrable on a bounded interval only if it's equal to a continuous function almost everywhere? I'd imagine this is the case, given the Riemann-Lebesgue lemma, which says that a function is RI iff its set of discontinuities has measure zero. (So the "continuous function" is then just f restricted to the complement of its set of discontinuities.) But I might be wrong. Help?