This is not actually a homework problem. Rather, it is a problem from Courant and Robbins' What is Mathematics?, Chapter 8: "The Calculus", page 409-410. 1. The problem statement, all variables and given/known data Prove that for any rational k =/= -1 the same limit formula, N → k+1, and therefore the result: ∫a to b xk dx = bk+1 - ak+1 / k+1 , k any positive integer remains valid. First give the proof, according to our model, for negative integers k. ... (There is more, but it's subsequent steps and, since I'm having trouble just getting started, I don't think it's relevant.) 3. The attempt at a solution I'm not really sure how to get started. That is, I'm not sure how to even introduce "negative integers" into the expression. Someone suggested I try a proof by substitution, allowing j to equal -k, but if k = 2 that takes us right back to the k =/= -1 thing, I think. A nudge in the right direction would be much appreciated.