7 The Riemann Integral

Finally, we can get to integrals. There are many ways to define an integral,

which can have some subtle differences. The definition we will use here is the

Riemann integral, which is the simplest definition, but is also the weakest one, in

the sense that many functions are not Riemann integrable but integrable under

other definitions.

Still, the definition of the Riemann integral is not too straightforward, and

requires a lot of preliminary definitions.