2.6.1.3 Fourier integral

Problem: Find the Fourier image of function \( f(x) \), if \( f(x) \equiv 0 \) when \( x \notin\left[x_{1}, x_{4}\right] \), and when \( x \in\left[x_{1}, x_{4}\right] \) the graph of this function consists of links of a polygonal chain, passing through points \( A\left(x_{1}, y_{1}\right), B\left(x_{2}, y_{2}\right) \), \( C\left(x_{3}, y_{3}\right), D\left(x_{4}, y_{4}\right) \). The coordinates of the points are presented in the table: \begin{tabular}{|c|c|c|c|} \hline\( A \) & \( B \) & \( C \) & \( D \) \\ \hline\( (0,-1) \) & \( (2,2) \) & \( (4,-1) \) & \( (5,-1) \) \\ \hline \end{tabular}