Let f:[1, ∞) → R be a differentiable function. If 6 ∫_1^x f(t) d t=3 x f(x)+x^3-4 for all x ≥ 1, then the value of f(2)-f(3) is

Let $\displaystyle f:[1, \infty) \rightarrow \mathbb{R}$ be a differentiable function. If $\displaystyle 6 \int_1^x f(t) d t=3 x f(x)+x^3-4$ for all $\displaystyle x \geq 1$, then the value of $\displaystyle f(2)-f(3)$ is