**5.3: The Fundamental Theorem of Calculus - Mathematics**
https://math.libretexts.org/Bookshelves/Calculus/Book%3A_Calculus_(OpenStax)/05%3A_Integration/5.3%3A_The_Fundamental_Theorem_of_Calculus

Jan 02, 2021 · f(c) = 1 b − a∫b af(x)dx. This formula can also be stated as. ∫b af(x)dx = f(c)(b − a). Proof. Since f(x) is continuous on [a, b], by the extreme value theorem (see section on Maxima and Minima), it assumes minimum and maximum values— m and M, respectively—on [a, b]. Then, for all x in [a, b], we have m ≤ f(x) ≤ M.

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