antiderivative velocity question

Question

A particle moves on a straight line and has acceleration a(t)=18t+14.

Its position at time t=0 is s(0)=6 and its velocity at time t=0 is v(0)=14.

What is its position at time t=7?

Answer 1

v(t) = ∫(18t + 14)dt = 9t² + 14t + C

v(0) = C = 14

v(t) = 9t² + 14t + 14

s(t) = ∫(9t² + 14t + 14)dt = 3t³ + 7t² + 14t + C

s(0) = C = 6

s(t) = 3t³ + 7t² + 14t + 6

s(7) = 1,029 + 343 + 98 + 6 = 1,476