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