11. (15 points) Let the sets be
$$
\begin{array}{l}
A=\left\{x \mid x^{2}+3 x+2 \leqslant 0\right\}, \\
B=\left\{x \mid x^{2}+a x+b \leqslant 0\right\} .
\end{array}
$$
(1) If $\left(\complement_{\mathrm{R}} A\right) \cap B=\{x \mid-1<x \leqslant 2\}$,
$$
\left(\complement_{\mathbf{R}} A\right) \cup B=\mathbf{R} \text {, }
$$

find the values of $a$ and $b$;
(2) If $b=1$, and $A \cup B=A$, find the range of real number $a$.
Three, 11. From the given, we have
$$
A=[-2,-1], \complement_{R} A=(-\infty,-2) \cup(-1,+\infty) \text {. }
$$

Let $f(x)=x^{2}+a x+b$.
(1) From $\left(\complement_{\mathrm{R}} A\right) \cap B=\{x \mid-10$, then
$$
\left\{\begin{array}{l}
\Delta>0, \\
f(-1) \geqslant 0, \\
f(-2) \geqslant 0, \\
-2 \leqslant-\frac{1}{a} \leqslant-1
\end{array}\right.
$$
$\Rightarrow a \in \varnothing$.
In summary, $-2<a \leqslant 2$.