If $f(t)=\{\begin{array}{ccc}-t& if& 0t<mn>2</mn>\\ 2t-6& if& 2t<mn>5</mn>\\ 3t-11& if& 5t\end{array},$ then $L\{f(t)\}(s)$ is equal to

A$.\frac{-1+(3-12s)e^{-2s}+(1-10s)e^{-5s}}{s^2}$

B$.-\frac{e^{-5s}+3e^{-2s}+1}{s^2}$

C$.\frac{-1+(12s-3)e^{-2s}+(10s-1)e^{-5s}}{s^2}$

D$.\frac{e^{-5s}-(4s-3)e^{-2s}-1}{s^2}$

E$.\frac{e^{-5s}+3e^{-2s}-1}{s^2}$