Question

F is bounded does not mean f is riemann integrable

Answer 1

Answer:

If f is a bounded function defined on a closed, bounded interval [a, b] then f is Riemann integrable if and only if the set of points where f is discontinuous has measure zero.

Answer 2

Hiiii dude......

Moreover, a function f defined on a bounded interval is Riemann-integrable if and only if it is bounded and the set of points where f is discontinuous has Lebesgue measure zero. An integral which is in fact a direct generalization of the Riemann integral is the Henstock–Kurzweil integral.