[SOLVED] Differentiation / Integration

Given the velocity and initial postion of a body moving along a coordinate line at time t, find the body's postion at time t.

$\displaystyle v = cos \frac{ \pi}{2}t, s(0)=1$

I am sure that my answer is wrong, i am thinking that if $\displaystyle s' = cos \frac{ \pi}{2}t$, then $\displaystyle s = sin \frac{ \pi}{2}t+c$, and if s(0)=1, then c=1 so $\displaystyle s = sin \frac{ \pi}{2}t +1$

But i know that if i were to differentiate that same expression, i would get something else not so? (chain rule)... so what should I do here?