The position of a particle at any time t >= 0 is given by p(t) = -t^3 + t^2 + 5t + 3. What is the displacement of the particle during the first four seconds?

I think this is just p(4) - p(0) = -25 - 3 = -28.

yes

the displacement is the final position - the original position, a vector. It is not the total distance moved.