I am asked to calculate the Fourier series of the following integral function:
$$F(t)=\int_0^\pi(\sin(t)+\sin(2t)-\frac{3}{2}\sin(4t))dt$$ Solving the integral it gives me:
$$F(t)=\frac{9}{8}-\cos(t)-\frac{1}{2}\cos(2t)+\frac{3}{8}\cos(4t)$$ Apparently, this is already the Fourier series of $F(x)$ (textbook's solution).
How can I deduce that?