Integrating a Riemann-integrable function gives a continuous primitive whose derivative recovers the integrand at continuity points.Suggest a slogan
Let \(a<b\), let \(f\colon[a,b]\to\RR\) be Riemann integrable on \([a,b]\), and define \(F\colon[a,b]\to\RR\) by \[ F(x)\coloneqq\int_a^x f(t)\,dt. \] Then \(F\) is continuous on \([a,b]\). If \(f\) is continuous at \(x_0\in[a,b]\), then \(F\) is differentiable at \(x_0\), one-sidedly if \(x_0\in\theset{a,b}\), and \(F'(x_0)=f(x_0)\). [@Rud76].