another question related to 2D histograms and integrals

OK, I can get a functionâ€™s (either TF1 or TF2) visualization as histogram with TF1->GetHistogram() â€“ but as far as I can follow the code [TF1:Paint ~line 2754] the functionâ€™s center value in the particular bin is used to fill the bin, or? Instead, I would like to use the integral of the function in the particular bin as value to be filled as bin content â€“ for example to tackle a bit better quite different gradients in a bin (if the binning is too coarse at extreme values or so).

So, is there a way to get a â€˜integral bin visualizationâ€™ of a function in Root?
If something like that exist, it would be great and would cure my todayâ€™s headache a bit

I thought that DrawIntegral() returns overall integral of the function, or?

What I am looking for is a way to draw the function itself in a histogram.
GetHistogram() fills the functionâ€™s value at a bin center as bin content. But I would like to fill the integral of the function in a bin as bin content â€“ similar as for fits when using option â€˜Iâ€™.

such function it does not exist but it is trivial for a user to implement and fill the histogram. Just do for example:

TF1 * f1 = new TF1("f","sin(x)",0,10);
TH1 * h1 = new TH1D(*((TH1D*) f1->GetHistogram()) );
for (int i = 1; i <= h1->GetNbinsX(); ++i)
h1->SetBinContent(i, f1->Integral( h1->GetXaxis()->GetBinLowEdge(i), h1->GetXaxis()->GetBinUpEdge(i) )/h1->GetBinWidth(i) );