Definition:Improper Integral/Half Open Interval/Open Below

Definition
Let $f$ be a real function which is continuous on the half open interval $\left({a \,.\,.\, b}\right]$.

Then the improper integral of $f$ over $\left({a \,.\,.\, b}\right]$ is defined as:


 * $\displaystyle \int_{\mathop \to a}^b f \left({t}\right) \rd t := \lim_{\gamma \mathop \to a} \int_\gamma^b f \left({t}\right) \rd t$

Also denoted as
It is common to abuse notation and write:
 * $\displaystyle \int_a^b f \left({t}\right) \rd t$

which is understood to mean exactly the same thing as $\displaystyle \int_{\mathop \to a}^b f \left({t}\right) \rd t$.