Đáp án:
$\begin{array}{l}
y = 2\sin x + 3\cos x + 1\\
\Rightarrow 2\sin x + 3\cos x = y - 1\\
Dk\,co\,nghiem:\\
{2^2} + {3^2} \ge {\left( {y - 1} \right)^2}\\
\Rightarrow {\left( {y - 1} \right)^2} \le 13\\
\Rightarrow - \sqrt {13} \le y - 1 \le \sqrt {13} \\
\Rightarrow 1 - \sqrt {13} \le y \le 1 + \sqrt {13} \\
\Rightarrow \left\{ \begin{array}{l}
GTNN:y = 1 - \sqrt {13} \\
GTLN:y = 1 + \sqrt {13}
\end{array} \right.
\end{array}$
