This has to do with the unit step function. The question is;
Sketch the function g(t) = 1 for 0<t<1 and is 0 for t>1.
Express g(t) in terms of the unit step function and hence or otherwise show that
L(g(t)) = 1/s^2 - e^-s (1/s^2 + 1/2)
The Attempt at a Solution
I sketched the graph (see attachment below). Im guessing the unit step function is t(u(t) - u(t-1)).
I tried one way of getting that answer like this t( u(t-1) u(t+1) - u(t-1) ). Obviously it didnt work out. I think I need to get u(t) in the form u(t-a) so I can use the table of Laplace transforms and just read out of it. How do I manipulate this kind of functions?