Let $f(x)=[x]\sin\bigg[\large\frac{\pi}{[x+1]}\bigg]$ where [.] denotes the greatest integer function. The domain of $f$ is and the point of discontinuity of $f$ in the domain are

Question

$(a)\;I-\{0\}\qquad(b)\;I-\{1\}\qquad(c)\;I-\{2\}\qquad(d)\;None\;of\;these$