Question

Given the velocity v=ds/dt and initial position of a body moving along a coordinate line, find the body's position at time t. v = sin(pi(t)) s(-6)=0. ...?

Answer 1

So lets see, I think the next formula can help you finding the body's position at time:
v(t)=s(t)=−(1/π)∗cos(π(t))+C s(t)=0 at t=-6 so C=(1/pi)
Saying this we do:s(t)=[−cos(π∗t)+1]/π
I think thic could help you through