*
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.