Riemann Integration

Abstract

We start with some notation. Consider a bounded function f on a closed and bounded interval [a,b]. The set P is said to be a partition of [a,b] if there is a natural n such that

$$P=\{x_0,x_1,\dots,x_n\} $$

where x ₀=a<x ₁<⋯<x _n =b. In words, P is a finite collection of ordered reals in [a,b] that contains a and b.