Answer
$s(t) = -cos(t) - sin(t) + 1$
Work Step by Step
$v(t) = -1(-sin(t)) - cos(t)$
$s(t) = -cos(t) - sin(t) + C$
Given: $s(0) = 0$
$s(0) = -cos(0) - sin(0) + C$
$0 = -1 - 0 + C$
$0 = -1 + C$
$C = 1$
Replace $C$ in the original function with the newly found value:
$s(t) = -cos(t) - sin(t) + 1$