I have two questions. [I'm referring to the main equation $J(x) = \operatorname{Li}(x)-\sum_\rho\operatorname{Li}(x^\rho)-\log2+\int_x^\infty\cfrac{dt}{t(t^2-1)\log t}$]
Question 1: The first two terms of the main equation are $\operatorname{Li}(x)$ and $-\sum_\rho\operatorname{Li}(x^\rho)$.
$\operatorname{Li}(x)$ is defined as $\int_2^x \frac{\mathrm dt}{\ln t}$. But in H.M. Edward's book he defines it as $\int_0^x \frac{\mathrm dt}{\ln t}$, which actually is $\operatorname{li}(x)$. So what definition is right?
Question 2: On page 30 in H.M. Edwards book, Edward implies that $$-\sum_\rho\operatorname{Li}(x^\rho) = -\sum_{\operatorname{Im}(\rho)>0}\operatorname{Li}(x^\rho)+\operatorname{Li}(x^{1-\rho}).$$ I have no idea why this equality holds. Please send me a link to a rigorous proof.