$\displaystyle g(x)=\left\{\begin{array}{cc}x^2+1,&\mbox{ if }x\leq 0\\x^2+bx\sin(\frac{1}{x})+c,&\mbox{ if }x>0\end{array}\right.$

Find all the values of b and c that make g continuous on R, express the values of b and c as sets.

$\displaystyle b\in$

$\displaystyle c\in$