Integrating $1/\theta$ over a range My textbook is telling me:
$$\int_{x}^{1} \frac{1}{\theta} d\theta = {|\log x|}$$
While I arrive at:
$$\int_{x}^{1} \frac{1}{\theta} d\theta = |\log(1)| - {|\log(x)|} = - {|\log(x)|}$$
Why am I wrong?
$0 < x < 1$
Edit: Here is a pic from the textbook


Your mistake is that the antiderivative of $\dfrac 1x$ is not $|\log x|$ but $\log x$. Then
$$\int_x^1\frac{dx}x=\log 1-\log x=-\log x$$ and in the particular case that $\log x <0$, this is also $|\log x|$.

The traditional solution is
$$\int_a^b\frac{dx}x=\log|b|-\log|a|.$$
I claim that it is technically more correct to write
$$\int_a^b\frac{dx}x=\log\frac ba.$$
