Laplace transform by definition.

Question

I have to find the Laplace transform by definition of
$ f(t) = \begin{cases} t^{2}, & 0\leq t\leq 1 \\ (t-1)^{-1}, & 1<t\leq 2 \\ 1, & 2<t\leq 3 \end{cases} $
But my doubt is in the interval $(3,\infty)$.