Let $f$ be a continuous function satisfying $\int_\limits{0}^{t^{2}}\left(f(x)+x^{2}\right) d x=\frac{4}{3} t^{3}, \forall t > 0$. Then $f\left(\frac{\pi^{2}}{4}\right)$ is equal to :

Question

$-\pi\left(1+\frac{\pi^{3}}{16}\right)$

$\pi\left(1-\frac{\pi^{3}}{16}\right)$

$-\pi^{2}\left(1+\frac{\pi^{2}}{16}\right)$

$\pi^{2}\left(1-\frac{\pi^{2}}{16}\right)$

Solution

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