已知函数 $f(x)$ 具有一阶连续导数且 $f(0) \neq 0$, 极限 $\lim _{x \rightarrow 0}\left[\frac{1}{\int_0^{x^2} f(t) \mathrm{d} t}-\frac{1}{x^2 f\left(x^2\right)}\right]=$
$\text{A.}$ $\frac{f^{\prime}(0)}{f^2(0)}$.
$\text{B.}$ $-\frac{f^{\prime}(0)}{f^2(0)}$.
$\text{C.}$ $\frac{f^{\prime}(0)}{2 f^2(0)}$.
$\text{D.}$ $-\frac{f^{\prime}(0)}{2 f^2(0)}$.