Consider a Fourier series of

$$-100S(x) = \sum_{n=1}^\infty b_n \sin(n\pi x)$$

where $S(x)$ is sigmoid function. The Fouerier coefficient is given by

$$b_n=2 \int_0^1 S(x) \sin(n\pi x)dx$$

Right?

If yes, what is the solution of this integral to calculate the Fourier coefficient for the above series?