Here are two spreadsheets for calculating the fraction of a blackbody’s radiant energy in a waveband between two wavelength limits. I used just brute-force numerical integration, which is readily comprehended, vs. the analytic form as an infinite series as given in the text.
Coarser form, not suited for a high fraction of flux in the ultraviolet:
Finer form, better for the case of high ultraviolet fraction.