​​​​​​​Đáp án:

Đặt \( x = 2018 - t \Rightarrow dx = -dt \),

\( \begin{cases} x = 0 \Rightarrow t = 2018 \\ x = 2018 \Rightarrow t = 0 \end{cases} \),

\( I = \int_{2018}^{0} \frac{1}{1 + f(2018 - t)} (-dt) = \int_{0}^{2018} \frac{dt}{1 + f(2018 - t)} \),

\( = \int_{0}^{2018} \frac{1}{1 + \frac{1}{f(t)}} dt = \int_{0}^{2018} \frac{f(t)}{f(t) + 1} dt = \int_{0}^{2018} dt - \int_{0}^{2018} \frac{1}{1 + f(t)} dt \),

\( \Rightarrow 2I = 2018 \Rightarrow I = 1009 \Rightarrow \boxed{C} \).