  Several second moment and other integral evaluations for the Riemann zeta
function $\zeta(s)$, Hurwitz zeta function $\zeta(s,a)$, and Lerch zeta
function $\Phi(z,s,a)$ are presented. Additional corollaries that are obtained
include previously known special cases for the Riemann zeta function
$\zeta(s)=\zeta(s,1)=\Phi(1,s,1)$. An example special case is: $$\int_R
{{|\zeta(1/2+it)|^2} \over {t^2+1/4}}dt=2\pi[\ln(2\pi)-\gamma],$$ with $\gamma$
the Euler constant. The asymptotic forms of certain fractional part integrals,
with and without logarithmic factors in the integrand, are presented.
Extensions and other approaches are mentioned.
