Bartle has a statement:
Although the absolute value of a proper Riemann integrable function is Riemann integrable, this may no longer be the case for a function which has an improper Riemann integral (for example, consider $f(x)=x^{-1} \sin(x)$ on the interval $1\le x\lt +\infty$).
Could I get a little help with this statement? I am assuming I need to show that the improper integral is integrable, but the absolute value is not.
Thanks.