Barrons AP Calculus - David Bock

(B) If a(t) = 20t^3 − 6t, then
v(t) = 5t^4 − 3t^2 + C 1 ,
s(t) = t^5 − t^3 + C 1 t + C 2 ,
Since
s(−1) = −1 + 1 − C 1 + C 2 = 2
and
s(1) = 1 − 1 + C 1 + C 2 = 4,
therefore
2 C 2 = 6, C 2 , = 3,
C 1 = 1.
So
v(t) = 5t^4 − 3t^2 + 1.