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# 1 Integrating real functions

After working through this section, you should be able to:

- appreciate how the Riemann integral is defined
- state the main properties of the Riemann integral
- appreciate how complex integrals can be defined.

In this section we define the Riemann integral of a continuous real function (named after Bernhard Riemann, whom we met in Session 1 for the Cauchy–Riemann equations) and outline its main properties. We then discuss complex integrals.

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