Let $f:R\rightarrow R$ be a differentiable function having $f(2)=6,f'(2)=\large\frac{1}{48}$.Then $\lim\limits_{x\to 2}\int_6^{f(x)}\large\frac{4t^3dt}{x-2}$ equals

Question

$(a)\;12\qquad(b)\;18\qquad(c)\;24\qquad(d)\;36$