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