We report on the first measurement of the rapidity distribution dsigma/dy over nearly the entire kinematic region of rapidity for e^+e^- pairs in the Z-boson region of 66<M_{ee}<116 GeV/c^2 and at higher mass M_{ee}>116 GeV/c^2. The data sample consists of 108 pb^{-1} of ppbar collisions at \sqrt{s}=1.8 TeV taken by the Collider Detector at Fermilab during 1992--1995. The total cross 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.