What remains is $y(t)=\cos(t-1)-\cos(t)$. Can this really be the response of a causal system to an input signal that starts at $t=0$? Maybe you forgot some important detail in your answer.
The correct answer must consist of $3$ different expressions for the time intervals $t<2$, $2<t<3$, and $t>3$. Your answer corresponds to one of those three expressions, so you need to add the other two, and the corresponding time intervals.