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Recognitions:      Gold Member        Science  Advisor     Staff Emeritus  No, amazingly, you are wrong and your teacher is right!    Since that integrand does not exist at x= 0, you have to use the definition: $$\int_{-1}^1 \frac{dx}{x}= \lim_{\alpha\to 0^-}\int_{-1}^\alpha \frac{dx}{x}+ \lim_{\beta\to 0^+}\int_\beta^1\frac{dx}{x}$$  and those limits do not exist.   You cannot just evaluate the anti-derivative at 1, -1, and then subtract- that's ignoring the whole problem of what happens at 1.
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