I have a question about a snippet on page 526 in the PRML book of Bishop.
Can someone explain to me why the right-hand side of equation (11.6) equals $z$?
It's unclear to me where this derivation comes from. Thanks for your help!
My first thoughts about this:
Plugging $p(z)=1$, in equation (11.5), we get $p(y)=|dz/dy|$.
Taking the integral of a derivative of $z$ (right-hand side), should give back the original $z$, leading to equation (11.6). However, where do the bounds $-\infty$ and $y$ of the integral come from?
It is mentioned that it is an indefinite integral, why do we have these bounds?
I also didn't take into account that there is an absolute value around $dz/dy$.
Can we just discard this as if it isn't there?