The FRWL models...
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The          integral can be solved analytically, if
Otherwise, numerically.  From         , one gets the comoving 
distance         , or in terms of physical units (e.g., Mpc):



This distance can then be used to evaluate the apparent 
diameters, magnitudes, volume densities, etc.  If                 ,




The apparent angular diameter is simply:



(because the universe expanded by 1+z since then).

For the apparent bolometric(!) luminosity:



One power of (1+z) comes from the rate of emission of photons, 
and the other from their energy change.  Sometimes D(1+z) is 
called the luminosity distance.

For more of the useful stuff, see the papers by Sandage (1988, 
ARAA 26, 561; and references therein), Stabell and Refsdal 
(1966, MNRAS 132, 379), or Solheim (1966, MNRAS 133, 321).