JEE Math Practice Question

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 :

1. A.$$-\pi\left(1+\frac{\pi^{3}}{16}\right)$$
2. B.$$\pi\left(1-\frac{\pi^{3}}{16}\right)$$
3. C.$$-\pi^{2}\left(1+\frac{\pi^{2}}{16}\right)$$
4. D.$$\pi^{2}\left(1-\frac{\pi^{2}}{16}\right)$$