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


The answer in the book is not wrong but is over-complicated.
The integral of $1/\theta$ in the positive real line is $\ln(\theta)$. Therefore
$$\int_x^1 1/\theta d\theta = \ln(1)-\ln(x)= -\ln(x)$$
However since $0<x<1$ (I suppose) we have that $\ln(x)$ is negative and so $-\ln(x) = |\ln(x)|$
