2.6.1.7 Fourier integral

Problem: Represent the following function as a Fourier integral, extending it evenly to the interval \( (-\infty, 0) \). \[ f(x)=\left\{\begin{array}{ll} 1, & \text { if } 0 \leq x \leq 1 \\ 0, & \text { if } x>1 \end{array} .\right. \]