10.4.2 Laplace transform

Problem: Find the Laplace transform of the function: \[ f(t)=\left\{\begin{array}{ll} 0, & t<0 \\ -2, & 0 \leq t<2 \\ 0, & 2 \leq t<3 \\ \frac{1}{2}, & 3 \leq t<5 \\ 0, & 5 \geq t \end{array}\right. \]