Tìm nguyên hàm \(F\left( x \right) = \int {\left( {x + \sin x} \right)dx} \) biết \(F(0)=19\).

A. \(F\left( x \right) = {x^2} + \cos x + 20.\)

B. \(F\left( x \right) = {x^2} - \cos x + 20.\)

C. \(F\left( x \right) = \frac{1}{2}{x^2} + \cos x + 20.\)

D. \(F\left( x \right) = \frac{1}{2}{x^2} - \cos x + 20.\)