\begin{definition}[Definition:Improper Integral/Open Interval]
Let $f$ be a real function which is continuous on the open interval $\openint a b$.
Then the improper integral of $f$ over $\openint a b$ is defined as:
:$\ds \int_{\mathop \to a}^{\mathop \to b} \map f t \rd t := \lim_{\gamma \mathop \to a} \int_\gamma^c \map f t \rd t + \lim_{\gamma \mathop \to b} \int_c^\gamma \map f t \rd t$
for some $c \in \openint a b$.
\end{definition}