To see how to handle the problem of an unbounded integrand, we start with the following special cases.
Cases where has an infinite discontinuity only at an interior point c, a <c < b are handled by writing
and using the definitions to see if the integrals on the right-hand side exist. If both exist then the integral on the left-hand side exists. If either of the integrals on the right-hand side diverges, then does not exist.