Có $y=sin^3xcosx-cos^3xsinx= sinxcosx(sin^2x-cos^2x)$$=\frac{1}2sin2x.(-cos2x)$
$=-\frac{1}2sin2x.cos2x$
$=-\frac{1}4.sin4x$
Có $-1\leq sin4x\leq1 \Rightarrow -\frac{1}4 \leq y \leq \frac{1}4$
$\Rightarrow \left\{ \begin{array}{l} GTNN=-\frac{1}4\\ GTLN=\frac{1}4 \end{array} \right.$