Fit histogram without option I

I’ve read the full documentation of TH1F::Fit and I’m a bit surprised about the option I: “Use integral of function in bin, normalized by the bin volume, instead of value at bin center”. I mean: why is this an option? This is the correct definition of chi^2 for an pdf fit. You can’t fit an histogram as you fit a TGraph for example.

I understand the performance point, but for example you can invert the logic: as default without the option I it computes correctly using the integral, with the option you fit with an approximate chi^2 using the value of the function at centerbin.