已知函数$f\left(x\right)=\left\{\begin{array}{c}x+1,-1\le x\le 0\\ \sqrt{1-x^2},0<x\le 1\end{array}\right.$,则${\int }_{-1}^{1}f\left(x\right)dx=$（   ）

阅读理解

    When the man's wife died，their youngest baby was 2 years old．They had six other children一three boys and three girls．aged from 4 t0 16．

    The man's parents and his wife's parents came to visit them．

    ‘‘We've been talking about how to make this work，”they said．“There's no way you can take care of all these children and work to make a living．So，we've decided to place each child with a different uncle and aunt．”

     The man refused．Over the next few weeks，he moved the family to a tiny town and his business developed quickly．People came from far away to do business with him．And the children helped him both at home and at work．

The children grew up and got married．Five of the seven went off to college．The children's success was a source of pride to the father．

    Finally，the youngest daughter，who was 2 years old when the mother died，got married．With his life's work done，the father died．

This man's work had been the lonely but joyful task of raising his family．This man was my father．I was the 1 6-year-old，the oldest of seven．

下列各式中，运算正确的是（   ）．

图中所示的是（）