If $\int\limits_0^x \, $f(t) dt = x2 + $\int\limits_x^1 \, $ t2f(t) dt then f '$\left( {{1 \over 2}} \right)$ is -

Question

If $\int\limits_0^x \, $f(t) dt = x² + $\int\limits_x^1 \, $ t²f(t) dt then f '$\left( {{1 \over 2}} \right)$ is -

${{18} \over {25}}$

${{6} \over {25}}$

${{24} \over {25}}$

${{4} \over {5}}$

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