Particle on a line question with integrals calc2 I have a question for calculus two regarding a particle on a line.

Question:
  A particle moves along a line with acceleration $a(t)=−1(t+3)~2\text{ft}/\text{sec}^2$. Find the distance traveled by the particle during the time interval $[0,1]$, given that the initial velocity $v(0)$ is $13~\text{ft/sec}$.

I think I'm supposed to use integrals, but I'm quite sure how to go about it. If anyone could help me out I'd be grateful, thank you <3

The velocity over $[0,1]$ is 
$$
v(t) = v(0) + \int_{0}^{t} a(x) \ dx
$$
The distance (not displacement) over this interval is 
$$
\int_{0}^{1} |v(t)| \ dt 
$$
So you can find the distance with two integrals.  It looks like your $a(t)$ is negative over $[0,1]$, but the initial velocity is much higher than $\int a(t) \ dt$ on that interval. 
