Derivatives and Integrals Robert Beezer beezer@pugetsound.edu Department of Mathematics and Computer Science University of Puget Sound June 20, 2013

We consider integrals of functions f(x). For example, \int_0^1\,\sin^2(x)\,dx

There is a remarkable theorem:

If f(x) is continuous, and the derivative of F(x) is f(x), then \int_a^b\,f(x)\,dx=F(b)-F(a)

Left to the reader.