Let $a,b \in \mathbb{R}$ with $a < b$, and let $f: [a,b] \to \mathbb{R}$ be Riemann integrable. For a tagged partition $(P,t)$ of $[a,b]$, write $P=\{x_0,x_1,\dots,x_n\}$ with $a=x_0<x_1<\cdots<x_n=b$, tags $t_i \in [x_{i-1},x_i]$, mesh $|P|=\max_{1\leq i\leq n}(x_i-x_{i-1})$, and Riemann sum