Let \(f(x)=\left\{\begin{array}{l}0, \text { if }-1 \leq x<0 \\ 1, \text { if } x=0 \\ 2, \text { if } 0<x \leq 1\end{array}\right.\) and let \(F(x)=\int_{-1}^{x} f(t) d t,-1 \leq x \leq 1\), then
(A) \(F\) is continuous function in \([-1,1]\)
(B) \(F\) is discontinuous function in \([-1,1]\)
(C) \(F^{\prime}(x)\) exists at \(x=0\)
(D) \(F^{\prime}(x)\) does not exists at \(x=0\)
Ans: (A, D)
