If $f(x)=p \sin x + q x \cos x + x^2$ and $f(2)=3$, find $f(-2)$

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A GRE subject trig question:

Let $p,q$ be constants and let $$f(x)=p \sin x + q x \cos x + x^2$$ for all real numbers $x$. If $f(2)=3$, find $f(-2)$.

So I plug in and obtain

$$3=\phantom{-}p \sin 2 +2q \cos 2 + 4$$ $$y=-p\sin 2 -2q \cos 2 + 4$$

Adding them, I obtain

$$3+y= 8$$

Where $y$ is what; that is, is the answer $5$?