ABSTRACT
In this chapter, the author gives a quick overview of Riemann integration. There are few real proofs but it is useful to have a quick tour before the author gets on with the job of extending this material to a more abstract setting. The author starts with a bounded function on a finite interval. This kind of function need not be continuous. Then select a finite number of points from the interval. For a positive function on the finite interval, the author constructs the area under the curve function. The author uses the Fundamental Theorem of Calculus to learn how to evaluate many Riemann integrals. The author calculates Riemann integrals of polynomials, combinations of trigonometric functions and so forth. Let’s formalize this as a theorem called the Cauchy Fundamental Theorem of Calculus.
