Module QAG in CMLIBAutomatic adaptive integrator, will handle many non-smooth integrands using Gauss Kronrod formulas.
CALL QAG(F, A, B, EPSABS, EPSREL, KEY, RESULT, ABSERR, NEVAL, IER, LIMIT, LENW, LAST, IWORK, WORK)| H2a1a1 | Automatic 1-D finite interval quadrature (user need only specify required accuracy), integrand available via user-defined procedure |