The fundamental theorem, Riemann sums and integral-defined functions

By the end you’ll be able to

• State and apply both parts of the fundamental theorem of calculus
• Differentiate functions defined by integrals with variable limits, e.g. $\frac{d}{dx}\int_{a(x)}^{b(x)} f(t)\,dt$, and differentiate under the integral sign
• Recognise limits of sums as Riemann sums and evaluate them as definite integrals