The velocity of a particle moving in a straight line is given by

v(t) = t² + 8.

(a)Find an expression for the position s after a time t. (Use C for the constant of integration.)

s(t) = ??????

(b)Given that s = 8 at time t = 0, find the constant of integration C.

C = ??????????

Find an expression for s in terms of t without any unknown constants.

s(t) = ???????????