Determine the Laplace transform of

$$f(t)=\{\begin{array}{lll}t,& \text{if}& 0t2\\ 8-3t,& \text{if}& 2\le t3\\ t-4,& \text{if}& 3\le t\le 4\\ 0,& \text{if}& 4t\end{array}$$

$$f(t)=\{\begin{array}{lll}t,& \text{if}& 0t2\\ 8-3t,& \text{if}& 2\le t3\\ t-4,& \text{if}& 3\le t\le 4\\ 0,& \text{if}& 4t\end{array}$$