The distance traveled over a time period is the integral of the speed

which is |v(t)|

the velocity v(t) is the integral of the acceleration.

Let's do it

a(t) = 2t + 5

so v(t) = t^2 + 5t + C

v(0) = -6 = C

So v(t) = t^2 + 5t - 6

We want the distance traveled between t= 0 and t =3

See the attachment note v(t) < 0 if t <1 so |v(t)| = -v(t) 0<t<1

and v(t) > 0 for t >1 so |v| = v(t) 1 < t < 3