I usually try to use Latex and make everything look pretty and easy to read, but Im in a bit of a rush so please excuse my ugly equations.

Im doing one-sided Laplace transforms involving unit step functions and Im not sure how to deal with one of the form f(x) * u(t) * u(c-t)

Explicitly my problem is:

f(t) = [2t^2 - 10t] * u(t) * u(2-t)

I know what the graph looks like, but Im not sure how to find F(s) in this situation.

Thanks in advance.