Let \( f(x) \) and \( g(x) \) be two functions satisfying \( f\left(x^{2}\right)+g(4-x)=4 x^{3}, g(4-x)+g(x)=0 \), then …

Let \( f(x) \) and \( g(x) \) be two functions satisfying \( f\left(x^{2}\right)+g(4-x)=4 x^{3}, g(4-x)+g(x)=0 \), then the value of \( \int_{-4}^{4} f\left(x^{2}\right) \mathrm{d} x \) is

[JEE Main 2021, 18 Mar (Shift 1)]