\begin{definition}[Definition:Definite Integral/Riemann/Integral Operator]
Let $\CC \closedint a b$ be the space of continuous functions.
Let $x \in \CC \closedint a b$ be a Riemann integrable function.
Let $\R$ be the set of real numbers.
The '''Riemann integral operator''', denoted by $I$, is the mapping $I : \CC \closedint a b \to \R$ such that:
:$\ds \map I x := \int_a^b \map x t \rd t$
where $\ds \int_a^b \map x t \rd t$ is the Riemann integral.
\end{definition}