I understand that the following function is the Fourier Sine Coefficient for the function. However, I am having trouble finding the function that can satisfy such conditions. How do I go about finding the function that satisfies the following conditions?
$$\int_0^L f(x) \sin(wx)dx=\begin{cases} 1, & \text{$0\leq w \leq 1$,}\\ 2, & \text{$1\leq w \leq 2$,}\\ 0, & \text{$w \geq 2.$} \end{cases}$$