By integrating the Fourier series equation $$y(x) = \frac{\pi}{2} - \frac{4}{\pi} \sum_{m=0}^{\infty} \frac{cos((2m+1)x)}{(2m+1)^2} $$
term by term from 0 to x, find the function $g(x)$ whose Fourier series is $$g(x) = \frac{4}{\pi} \sum_{m=0}^{\infty} \frac{sin((2m+1)x)}{(2m+1)^3} $$
I don't understand how the negative sign in front of the series in the first equation turns positive, or how the $\frac{\pi}{2}$ disappears/ goes into the series somehow?