1. Given the function $f(x)=\frac{\sqrt{2} \sin \left(x+\frac{\pi}{4}\right)+2 x^{2}+x}{2 x^{2}+\cos x}$ has a maximum value $M$, and a minimum value $m$, then the value of $M+m$ is
1. 2 Detailed Explanation: $f(x)=\frac{\sin x+\cos x+2 x^{2}+x}{2 x^{2}+\cos x}=\frac{\sin x+x}{2 x^{2}+\cos x}+1, g(x)=\frac{\sin x+x}{2 x^{2}+\cos x}$ is an odd function. $g(x)_{\max }=-g(x)_{\min }$, and $M=g(x)_{\max }+1, m=g(x)_{\min }+1$, so $M+m=2$.