Let \( g \) a differentiable function satisfying P \( \int_{0}^{x}(...

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Let \( g \) a differentiable function satisfying
P \( \int_{0}^{x}(x-t+1) g(t) d t=x^{4}+x^{2} \) for all \( x \geq 0 \). The value

W of \( \int_{0}^{1} \frac{12}{g^{\prime}(x)+g(x)+10} d x \) is equal to:
(1) \( \frac{\pi}{6} \)
(2) \( \frac{\pi}{3} \)
(3) \( \frac{\pi}{4} \)
(4) \( \frac{\pi}{2} \)
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