Answer
$25$
Work Step by Step
Recall the limit rules:
$ \ Rule \space1 : \lim\limits_{x \to a} [A(x)]^n =[\lim\limits_{x \to a} A(x)]^n $
$\ Rule \space2 : \lim\limits_{x \to a} A(x)=A(a)$
$\ Rule \space3: \lim\limits_{x \to a} \dfrac{A(x)}{B(x)}=\dfrac{\lim\limits_{x \to a} A(x)}{\lim\limits_{x \to a} B(x)}$
Apply Rules: $(1)$ and $(2)$
$\lim\limits_{x \to a} [A(x)]^n =[\lim\limits_{x \to a} A(x)]^n $ and $ \lim\limits_{x \to a} A(x)=A(a)$
$\lim\limits_{x\to -2}(x^2+1)^2\\
=\left[(-2)^2+1\right]^2 \\=(4+1)^2 \\=5^2 \\=25$
