Answer
The integral does not exist.
Work Step by Step
$\int_{-1}^{2} \frac{4}{x^3}~dx$
The graph of $~~\frac{4}{x^3}~~$ has a vertical asymptote at the point $x=0$. Therefore, the function is not continuous on the interval $[-1,2]$ and we can not apply the Fundamental Theorem to calculate the value of this integral.
The integral does not exist.