Calculus, 10th Edition (Anton)

$$s(t) = 2+\sin t$$
Given $v(t) =\cos t$ , $s(0)=2$ Since \begin{align*} s'(t)&=v(t)\\ s(t)&=\int v(t)dt\\ &=\int \cos t dt\\ &=\sin t+c \end{align*} Since $s(0)=2$, then $c=2$, and $$s(t) = 2+\sin t$$