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To Rene Brune,
As reference to this link: https://root.cern.ch/root/roottalk/roottalk03/2211.html
I wonder if you noticed in this code that "xmin- axis->GetBinLowEdge(bmin) " can give 0 value since xmin and low edge number of bmin can be same or 0 for instance.
I feel like the rule when finding the integral is not obeyed. What do you think it refers when it says xmin and axis->GetBinLowEdge(bmin) separately?
Check the attachment and formula 5.38, please.
Thanks. 
You know what I just tried that code I mentioned on a data, and the first deduction part from integral equals to 0 , and second deduction part from integral is equal to = h1->GetBinContent(bin_Upper) indeed.
Does “the way code calculates the integral” still make any sense? Nope. Integral is just double integral = h->Integral(bmin,bmax). However, he was , I guess, trying to deduce some background which only he, himself, understands.