Suppose $f:R\rightarrow R$ is a differentiable function and $ f(1)=4$.Then value of $\lim\limits_{x\to 1}\int\limits_4^{f(x)}\large\frac{2t}{x-1}$$dt$ is

Question

$(a)\;8f'(1)\qquad(b)\;4f'(1)\qquad(c)\;2f'(1)\qquad(d)\;f'(1)$