I want to ask if the indicator function of rational numbers is Riemann-integragle, cause I read that a function is Riemann-integrable if the set of discontinuities is at most of Lebesgue measure $0$ on a compact set, And $\mathbb{Q}$ has zero Lebesgue measure. However I also read arguments about the non integrability using Darboux sums, so it is not clear for me if it is integrable or not.
Thanks.