We report two complementary measurements of the diboson (WW + WZ) cross section in the final state consisting of an electron or muon, missing transverse energy, and jets, performed using p anti-p collision data at s**(1/2) = 1.96 TeV collected by the Collider Detector at Fermilab. The first method uses the dijet invariant mass distribution while the second method uses more of the kinematic information in the event through matrix-element calculations of the signal and background processes and has a higher sensitivity. The result from the second method has a signal significance of 5.4 sigma and is the first observation of WW + WZ production using this signature. Combining the results from both methods gives sigma_WW+WZ = 16.0 +/- 3.3 pb, in agreement with the standard model prediction.
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