*Fundamental Theorem of Calculus II*

Let f be an integrable function on [a, b]. For x in [a, b], let F(x) be the integral of f(x) from a to x. Then F is continuous on [a, b]. If f is continuous at x

_{0}in (a, b), then F is differentiable at x

_{0}and F'(x

_{0}) = f(x

_{0}).

Note that FTC I (above w/u) does not imply FTC II and FTC II does not imply FTC I, and so are not equivalent definitions.