This problem involves an object moving along a horizontal line, where its velocity $v(t)$ is given as a cubic function:

$v(t) = t^3 + 31t^2 - 32t \quad \text{m/s}$

over the interval $-1 \leq t \leq 3$ seconds.

Are you looking to compute something specific related to the velocity function, such as displacement, acceleration, or something else? Let me know how you would like to proceed!