The "integration to zero" effect the author observes is a consequence of the fact that the Fourier Transform is meant only for periods signals. Practically, we all often toss any time series data into an FFT to get a look at it in frequency space, but the math is only exactly correct with the time series samples used from one cycle of a period signal that repeats forever.

By generating the frequency domain Fourier coefficients and then transforming them to the time domain, the author is guaranteed to get a signal that starts and ends at the same value, because the transformation assumes it's a periodic signal and so the first and last values of the period must be the same.