Here is problem number one.

g(t) = 2t for 0 <= t < 1;

2 for 1 <= t;

This is the same as:

g(t) = 2tH(t) - 2tH(t-1) + 2H(t-1)

The next step is were I'm confused. The book finished setting up this problem for a laplace transform by changing the equation to this:

g(t) = 2tH(t) - 2(t-1)H(t-1)

Why did they change it like this and how did they do this. I'm know I'm over looking something but, I'm not sure what. Any help would be great.