Why there is so large a gap between the experimental data and the integral of fitting function?

The previous remarks explain the large discrepancy but in general there can be more subtle issues. Normally a fit tries to minimize the distance between the histogram bin height and the value of the fitting function in the center of the bin. The resulting fit function will also deliver the optimal integral as long as the fit function is linear across the bin. In order to make sure that your fit has the correct integral, you should specify the fit option “I”