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
in (a, b), then F is differentiable
) = f(x0
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.