已知函数 $f(x) = \left\{ \begin{array}{ll} 2(x - 1), & x < 1, \\ \ln x, & x \geqslant 1, \end{array} \right.$ 则 $f(x)$ 的一个原函数是（ $\left(\mathrm{A}\right)F(x)=\left\{\begin{array}{ll}\left(x-1\right)^{2},&x< 1,\\ x(\ln x-1),&x\geqslant 1.\end{array}\right.$ $\left(\mathrm{B}\right)F(x)=\left\{\begin{array}{ll}\left(x-1\right)^{2},&x< 1,\\ x(\ln x+1)-1,&x\geqslant 1.\end{array}\right.$ $\left(\mathrm{C}\right)F(x)=\left\{\begin{array}{ll}\left(x-1\right)^{2},&x< 1,\\ x\left(\ln x+1\right)+1,&x\geqslant 1.\end{array}\right.$ $\left(\mathrm{D}\right)F(x)=\left\{\begin{array}{ll}\left(x-1\right)^{2},&x< 1,\\ x(\ln x-1)+1,&x\geqslant 1.\end{array}\right.$