Mathematica is performing a substitution to transform the integral, which consequently changes the bounds of integration. This transformed integral does not converge.

When evaluating an integral, Mathematica applies a series of change-of-variables substitutions in attempt to put this integral in a standard from. Likely ehat has happened here is that Mathematica has performed a substitution like $t\to -t$ which has the effect of changing the bounds of integration. The resulting integral does not converge which almost certainly means that your original integral doe snot converge either. If you have reason to believe that your integral does converge, you could try integrating term by term.