If f is a reimann integrable function on [a,b], and if [c,d] is a subset of [a,b], prove that f is reimann integrable on [c,d]
hint: if P is any partition of [c,d], P can be extended to a partition P* of [a,b] with ||P*|| <= ||P||. Show that
U(f,P) - L(f,P) <= U(f,P*) - L(f,P*)