We report on the first measurement of the rapidity distribution d sigma/dy over nearly the entire kinematic region of rapidity for e+ e- pairs in the Z-boson region of 66 < M_ee < 116 GeV/c2 and at higher mass M_ee > 116 GeV/c2. The data sample consists of 108 pb-1 of p anti-p collisions at s**(1/2) = 1.8 TeV taken by the Collider Detector at Fermilab during 1992-1995. The total section in the Z-boson region is measured to be 252 +/- 11 pb. The measured total cross section and d sigma/dy are compared with quantum chromodynamics calculations in leading and higher orders (CDF Note 5422).