Lebl-Basic-Analysis-I · Problem 5.3.4

The Riemann Integral

Mathematics · fundamental-theorem-of-calculus

Problem

Let f:[a,b]→Rf : [a,b] \to \mathbb{R} be a continuous function. Let c∈[a,b]c \in [a,b] be arbitrary. Define F(x):=∫cxf.F(x) := \int_c^x f. Prove that FF is differentiable and that F′(x)=f(x)F'(x) = f(x) for all x∈[a,b]x \in [a,b].

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