Given a function f deﬁne a new function Sf(x) by summing up all values of f(hj) where 0 ≤ jh < x. That is, if k is such that kh is the largest below x, then Sf(x) = h[ f(0) + f(h) + f(2h) + .... + f(kh) ] We call Sf also the ”integral” or ”antiderivative” of f. The teacher who wrote the lecture notes I'm reading through gives an example of integration. He evaluates Sf(x) for f(x)=1. I don't understand the first sentence: We have Sf(x) = 0 for x ≤ h. Why? Sorry for being such a n00b, but I don't understand. Please help me. Thanks, Mathguy By the way, he verifies that the js in the definition are integers.