Fundamental theorem of calculus (idea)

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 x₀ in (a, b), then F is differentiable at x₀ and F'(x₀) = 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.