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数学公式:​

Let f ⁣:[a,b]→Rf\colon[a,b]\to\R be Riemann integrable. Let F ⁣:[a,b]→RF\colon[a,b]\to\R be F(x)=∫axf(t) dtF(x)=\int_{a}^{x} f(t)\,dt. Then FF is continuous, and at all xx such that ff is continuous at xx, FF is differentiable at xx with F′(x)=f(x)F'(x)=f(x).