Cho \(I = \int\limits_0^1 {\frac{x}{{{x^2} + 1}}dx} \). Bằng cách đặt \(t = {x^2} + 1\) thì

A. \(I = \frac{1}{2}.\int\limits_1^2 {\frac{{dt}}{t}} \)

B. \(I = \int\limits_0^1 {\frac{{dt}}{t}} \)

C. \(I = \frac{1}{2}.\int\limits_0^1 {\frac{{dt}}{t}} \)

D. \(I = \int\limits_1^2 {\frac{{dt}}{t}} \)