Hướng dẫn giải

\[I = \int\limits_0^{\frac{\pi }{2}} {\left[ {f\left( x \right) + 2\sin x} \right]dx = \int\limits_0^{\frac{\pi }{2}} {f\left( x \right)dx} + 2\int\limits_0^{\frac{\pi }{2}} {\sin xdx} = 5 - 2\cos x\left| {_{\scriptstyle\atop\scriptstyle0}^{\frac{\pi }{2}}} \right. = 7.} \]

Chọn D.