Well, you will need to check how you fill your histogram as Impact_mu_A->Print("all"); shows big bin errors:
TH1.Print Name = Impact_mu_A, Entries= 4, Total sum= 2867.37
fSumw[0]=0, x=-0.5, error=0 # the underflow bin
fSumw[1]=645.963, x=0.5, error=645.963
fSumw[2]=2221.41, x=1.5, error=1286.41
fSumw[3]=0, x=2.5, error=0
(...)
fSumw[100]=0, x=99.5, error=0
fSumw[101]=0, x=100.5, error=0 # the overflow bin
BTW. You probably want (excluding underflow and overflow bins):
Double_t error_A;
Double_t A = Impact_mu_A->IntegralAndError(1, Impact_mu_A->GetNbinsX(), error_A, ""); // "" or "width"
or (including underflow and overflow bins):
Double_t error_A;
Double_t A = Impact_mu_A->IntegralAndError(0, (Impact_mu_A->GetNbinsX() + 1), error_A, ""); // "" or "width"