Let $f(x)=\lim _{\boldsymbol{\theta} \rightarrow 0}\left(\frac{\cos \pi x-x^{\left(\frac{2}{\boldsymbol{\theta}}\right)} \sin (x-1)}{1+x^{\left(\frac{2}{\boldsymbol{\theta}}\right)}(x-1)}\right), x \in \mathbf{R}$. Consider the following two statements : (I) $f(x)$ is discontinous at $x=1$. (II) $f(x)$ is continous at $x=-1$. Then,