Let f:[0,1]-> R be bounded on [0,1] and continuous on (0,1). Prove that f is Riemann integrable on [0,1]. Hint: Show that for any epsilon > 0 there exists a partition P of [0,1] such that U(f,P)-L(f,P) < epsilon.
So Let P = {0 = t0 < t1 < ... < tn = 1}
Since its bounded on [0,1] (|f(x)| <= S)...