Answer
Diverges.
Work Step by Step
The integrand has a discontinuity at$ c=0\in[-2,3]$. Type 2c.
$\displaystyle \int_{a}^{b}f(x)dx=\int_{a}^{c}f(x)dx+\int_{c}^{b}f(x)dx$
$I=\displaystyle \int_{-2}^{3}\frac{dx}{x^{4}}=\int_{-2}^{0}\frac{dx}{x^{4}}+\int_{0}^{3}\frac{dx}{x^{4}}=I_{1}+I_{2},$
$I_{1}= \displaystyle \int_{-2}^{0}\frac{dx}{x^{4}}$ is a type 1 improper integral and
$I_{1}=\displaystyle \lim_{t\rightarrow 0^{-}}\left[-\frac{x^{-3}}{3}\right]_{-2}^{t}=\displaystyle \lim_{t\rightarrow 0^{-}}\left[-\frac{1}{3t^{3}}-\frac{1}{24}\right]=\infty$,
$I_{1}$ diverges.
So, I diverges.
