If you represent the spectral peak as some functional form (Gaussian, Loretnz, etc.), you could probably analytically (or semi-numerically) work out a connection between FWHM and area under curve for a specified frequency range. This wold be true if the parameterization fixed the shape of the curve given just the parameter FWHM. Then, the area is obtained by integrating this curve over desired frequency range. Of course, this will not be very accurate in general (unless your spectrum is well modeled by the analytical form). Else, you could use a sum of Gaussians, and do a fit. Easier to just numerically integrate your actual spectrum.