Laplace II: Steps, Impulses & Convolution · Superchallenge problem

A system with a one-second memory window obeys $y'(t)=-\displaystyle\int_{\max(0,\,t-1)}^{t}y(\tau)\,d\tau$ with $y(0)=1$. Writing the right side as a convolution with the box $u(t)-u(t-1)$, use the Laplace transform to find $y(2)$. Give an exact answer.