Origin allows you to fit the peaks from the result of frequency count. Also, fitted curves can added into the new layer in the Histogram.
Copy and paste the sample data into Origin and set the column as Y (Highlight the column and choose Column: Set As: Y from the Origin menu). Plot this data as a Histogram by clicking Plot > Basic 2D: Histogram from the menu.
If your baseline is complicated, or if you would like Origin to auto find peaks by specified method, please use Peak Analyzer (open from Analysis: Peaks and Baseline: Peak Analyzer). Note that Peak Analyzer provides powerful controls appropriate not just in two cases mentioned.