Indefinite Integration problem

[QuarkCharmer]

Homework Statement

A particle is moving with the given data. Find the position of the particle.
$a(t)=t^{2}-4t+6$,
$s(0)=0$,
$s(1)=20$

Homework Equations

The Attempt at a Solution

$a(t)=t^{2}-4t+6$, $s(0)=0$, $s(1)=20$
$$v(t)=\int t^{2}-4t+6 dt$$
$$v(t)=\frac{t^{3}}{3}-2t^{2}+6t+C_{1}$$
Then I suppose I take the antiderivative again to get to s (distance), I can't solve for the constant yet.

$$s(t)=\int \frac{t^{3}}{3}-2t^{2}+6t+C_{1} dt$$
$$s(t)=\frac{t^{4}}{12}-\frac{2t^{3}}{3}+3t^{2}+C_{1}t+C_{2}$$

So now I have two constants in there? Would I just use the parameters $s(0)=0$ and $s(1)=20$ to try to solve this like a system of 2 equations with two unknowns? I don't really know how to proceed. The other problems like this at least gave me a value for the first derivative of the original function so I could sort of work backwards.

 

[ideasrule]

So now I have two constants in there? Would I just use the parameters $s(0)=0$ and $s(1)=20$ to try to solve this like a system of 2 equations with two unknowns?

This is exactly what you do. Be more confident!