As suggested by John, if you want the Cumulative Distribution Function of a standard function, using a specific solution would be a better approach. He pointed out DCDFLIB. GSL has a very large number of specific CDFs, hidden in Chapter 19, "Random Number Distributions".
To do numerically evaluate the CDF of a unusual function, there are several choices in GSL, e.g., gsl_integration_qag for an integral from a to b, or gsl_integration_qagiu, which does semi-infinite integrals from a to +infinity.