Determine the values of b and c so that the following function is continuous:

$\displaystyle f(x) = \left\{\begin{array}{cc}x+1,&\mbox{ if }

1< {x}< 3\\x^2 + bx + c, & \mbox{ if } \lvert x+2 \rvert \geq 1\end{array}\right$

Restating this function to remove the absolute values, I get:

$\displaystyle f(x) = \left\{\begin{array}{cc}x^2 + bx + c,&\mbox{ if }

{x}\leq -3\\ x^2 + bx + c, & \mbox{ if } x \geq -1\\x + 1 , &\mbox{ if } 1 < x < 3 \end{array}\right$

But this makes absolutely no sense to me since I can see no way that this function can be continuous defined like I have done it. I must be screwing up the absolute value inequality.

Can somebody help?

Thanks.