$\int \limits_0^{x^2} t.f(t).dt =\large\frac{2}{5}.$$x^3$ then find $f\bigg(\large\frac{4}{25}\bigg)$

Question

$$\begin {array} {1 1} (a)\;\frac{4}{\sqrt 5} \\ (b)\;\frac{2}{5} \\ (c)\;\frac{\sqrt 2}{5} \\ (d)\;\frac{\sqrt 2}{5} \end {array}$$