find the laplace transform of the function :

$$f(t) =\begin{cases}
t^2, & 0<t<1 \\
2\cos t+2, & t>1 \\
\end{cases}$$

My attempt:

$$L\{f(t)\}=\int\_{0}^{1}e^{-st} \ t^2 \ \text{d}t+\int\_{1}^{\infty}e^{-st} \ (2\cos t+2) \ \text{d}t$$

Now,
$$\int\_{0}^{1}e^{-st} \ t^2 \ \text{d}t=\frac{-1}{s}e^{-s}-\frac{2}{s}te^{-s}-\frac{2}{s^3}e^{-s}+\frac{2}{s^3}$$

And

$$\int\_{1}^{\infty}e^{-st} \ (2\cos t+2) \ \text{d}t$$

But the integration is not stopping.