Originally Posted by
durrrrrrrr Let h be a bounded function in [a,b] and let c be a point in [a,b]. Prove that for all e>0, there exists d>0 such that for every partition P of the [a,b] with parameter m(P)<d the following is true:
|U(h,Q)-U(h,P)|<e
where U(h,R) is the upper Darboux sum of h according to the partition R,
and Q is the union of P and {c}.
I think I can do most of the question myself, but I get stuck at the end. I'm not sure how to complete the proof for a case where c is a discontinuity of point of h.
Thanks for help in advance.