Mathematics Question from JEE Main 2025 · 28 January, Shift 2

Let $f : \mathbb{R} \to \mathbb{R}$ be a twice-differentiable function such that $f(2) = 1$. If $F(x) = x f(x)$ for all $x \in \mathbb{R}$, and the integrals $\int_0^2 x F'(x) \, dx = 6$ and $\int_0^2 x^2 F''(x) \, dx = 40$, then $F'(2) + \int_0^2 F(x) \, dx$ is equal to: