设三个积分分别为
$$
\begin{gathered}
\mathrm{M}=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin x}{1+x^2} \cos ^4 x \mathrm{~d} x, \\
N=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\sin ^3 x+\cos ^4 x\right) \mathrm{d} x, \\
P=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^2 \sin ^3 x-\cos ^4 x\right) \mathrm{d} x,
\end{gathered}
$$
则