If \(f(x)=\left\{\begin{array}{cc}\int_0^x(5+|1-t|) d t, & x>2 \\ 5 x+1, & x \leq 2\end{array}\right.\), then…

\(f(x)\) is not continuous at \(x=2\)

\(f^{\prime}(x)\) is not differentiable at \(x=1\)

\(f(x)\) is continuous but not differentiable at \(x=2\)

\(f(x)\) is everywhere differentiable