\begin{definition}[Definition:Riemann Sum]
Let $f$ be a real function defined on the closed interval $\mathbb I = \closedint a b$.
Let $\Delta$ be a subdivision of $\mathbb I$.
For $1 \le i \le n$:
:let $\Delta x_i = x_i - x_{i - 1}$
:let $c_i \in \closedint {x_{i - 1} } {x_i}$.
The summation:
:$\ds \sum_{i \mathop = 1}^n \map f {c_i} \Delta x_i$
is called a '''Riemann sum''' of $f$ for the subdivision $\Delta$.
\end{definition}