Given a function \( g \), continuous everywhere such that \( g(1)=5...

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Given a function \( g \), continuous everywhere such that \( g(1)=5 \) and \( \int_{0}^{1} g(t) d t=2 \). If
\( \mathrm{P} \)
W \( f(x)=\frac{1}{2} \int_{0}^{x}(x-t)^{2} g(t) d t \), then compute the value of \( f^{\prime \prime \prime}(1)-f^{\prime \prime}(1) \)
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