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:
[tex]\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}[/tex]
and those limits do not exist.
You cannot just evaluate the antiderivative at 1, 1, and then subtract that's ignoring the whole problem of what happens at 1.
