What property of Riemann integrals in general that makes it not complete?

Question

I know that I can find a sequence of functions that are Riemann integrable but converges to a function f that is not Riemann integrable and this would show that the space of all Riemann integrable functions is not complete. but what property of the space that makes it true abstractly. Is it because $$\lim_{n\to \infty}\int_{a}^{b} f_{n} dx =\int_{a}^{b} f dx $$ iff $f_{n} \to f$ uniformly not point-wise . while the above property in Lebesgue integrals could be true with point-wise convergence only? I mean, In general why Lebesgue integrable functions form a complete space but not all the Riemann integrable functions can?