7. Let f : [a, b] ---; R, a = Xo < Xl < ... < Xn =

b, and suppose that f(Xk+) exists and is finite for k = 0,1, ... , n-1 and f(Xk-) exists and is finite for k = 1, ... , n.

Show that if f is continuous on each subinterval (Xk-l, Xk), then f is integrable on [a, b] and Ib n l xk a f(x) dx = ~ Xk-l f(x) dx.