Problem $1(1+2=3$ points$)$: Consider an LTI system whose impulse response is the following pulse

$t-1$

$($a$)$ Find the Laplace transform of $h(t),$ i$.$e$.,H(s).$

$($b$)$ Using Convolution, carefully sketch the output of the system $y(t),$ if the input $x(t)$ is the following pulse:

a$)$

$\frac{}{1}$

$2\frac{17}{2}$

$H(s)=\frac{2e^5}{s}-\frac{2e^{25}}{s}$