Integral inside a TCutG

Can anyone supply their ideas on how one can find the integral of a TH2 inside a graphical TCutG?

I am doing it in the following manner, but am not convinced that the integral returned is correct.

Double_t mg1_counts_cond = mg1->Integral(h2);

where h2 is of type TH2 and mg1 is of type TCutG.

Any ideas appreciated.

This is correct, check your cut region with h2->Draw(Form("[%s]", mg1->GetName()))