1. Introduction
Riemann integration is one of the most popular and widely-used tool in modern mathematics and areas that require advanced mathematics. We first provide a quick review on Riemann integration.
Definition 1.1 (Partition)
Suppose \(a,b\in \mathbb{R}\) with \(a<b\). A partition of \([a,b]\) is a finite list of the form \(x_0,x_1,\dots,x_n\), where
$$
a=x_0< x_1< \dotsb< x_n=b.
$$
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