The impulse response a the system is $h(t)=t\:u(t).$ For an input $u(t-1)$, the output is
1. $\frac{t^2}{2}u(t)$
2. $\frac{t(t-1)}{2}u(t-1)$
3. $\frac{(t-1)^2}{2}u(t-1)$
4. $\frac{t^2-1}{2}u(t-1)$