Rules

v(t)=ds/dt

a(t)=dv/dt

v(t) = t^2+3t+C

C = -6

v(t) = t^2+3t-6

s(t) = t^3/3+3t^2/2-6t+D

D = 3

s(t) = t^3/3+3t^2/2-6t+3

a = 2t + 3

Integrating gives

v = t^2 + 3t + c

But v(0) = -6

-6 = c

v = t^2 + 3t - 6

Integrating gives

s = (t^3/3) + (3/2)t^2 - 6t + c

but s(0) = 3

3 = c

s = (t^3)/3 + (32)t^2 - 6t + 3