Can somebody explain to me, geometrically and intuitively, the fundamental theorem of calculus? I understand that i can find the area between the graph of f'(x) and the x axis where b>x>a by finding f(b)-f(a), but i dont understand why. Suppose something is too hard to integrate. Can i use the riemann sum to estimate the area of an interval as closely as possible, and then use that approximation to help me integrate? Im sure that it must be possible, but i dont know how.