y(t) having u(t) and function transfer

I have a exercise and i can't do a part of it. I've a transfert function G(s) = 1/(s+1) and u(t), the entering signal:<pre>
1+2t for 0<=t<1
u(t) =
t-1 for t>=1

I have to find y(t), the outcoming signal of the system.

I find, correctly, the signal y(t) about the first part of u(t), 1+2t:
y1(t)=2t + e^{-t} -1

First i use laplace antitransform on u(t), for have U(s)
Second Y(s)= G(s)U(s)
Antitransform Y(s) for have y(t)</pre>
But now i don't know how to find y(t) for the second part, t-1. Could someone help to find it, i'd like to comprend.

Thanks!