Laplace transformation of a piecewise function?

Question

So I know in general how to do the laplace transformation of piecewise functions, but I ran into a different kind of piecewise than I have been doing so far.

So I know for a function like:

I just need to do this:

But what am I supposed to do for a piecewise function like this?:

I just want to know how to write out the second piecewise question just like the first one, I know how to do the steps after. Thanks in advance!