\begin{definition}[Definition:Improper Integral]
An '''improper integral''' is a definite integral over an interval which is not closed, that is, open or half open, and whose limits of integration are the end points of that interval.
When the end point is not actually in the interval, the conventional definition of the definite integral is not valid.
Therefore we use the technique of limits to specify the integral.
'''Note:''' In the below, in ''all'' cases the necessary limits must exist in order for the definition to hold.
\end{definition}