\( \lim _{x \rightarrow 0} \frac{\int_{0}^{x^{2}}\left(\tan ^{-1} t\right)^{2} d t}{\int_{0}^{x^...

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\( \lim _{x \rightarrow 0} \frac{\int_{0}^{x^{2}}\left(\tan ^{-1} t\right)^{2} d t}{\int_{0}^{x^{4}} \sin \sqrt{t} d t} \) is equal to
(a) 1
(b) -1
(c) \( \frac{-1}{2} \)
(d) \( \frac{1}{2} \)
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