trigonometric series "f(x)=x" $-2<x<2$ odd extensions

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I plan it as follows:

$a0=\frac{1}{\pi 2}\int _{-2}^2x\cdot dx\:$

$an=\frac{1}{\pi }\int _{-2}^2x\cdot \:cos\left(nx\right)dx\:$

$bn=\frac{1}{\pi }\int _{-2}^2x\cdot \:sin\left(nx\right)dx\:$

But my teacher says that the argument (nx) is wrong in an. I do not understand why? I think that being odd an=0. But the integral as it is correct?. Thanks for the help I have exam tomorrow

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Note $L=2$ thus $$a_0=\frac{1}{4}\int_{-2}^{2}xdx=0$$ $$a_n=\frac{1}{2}\int_{-2}^{2}x\cos\left(\frac{n\pi x}{2}\right) dx$$ $$b_n=\frac{1}{2}\int_{-2}^{2}x\sin\left(\frac{n\pi x}{2}\right) dx$$