Which of the following statements is sufficient to guarantee that there exists a number c in [a,b] for which f(c) equals the average value of a real-valued function f on that interval?
a) f is differentiable on (a,b).
b) f is continuous on the closed interval [a,b].
c) f is Riemann–integrable on [a,b] even if it has jump discontinuities.
d) f is continuous only on the open interval (a,b).