We present a measurement of σ(pp→W)×B(W→eν) at s√=1.96  TeV, using electrons identified in the forward region (1.2<|η|<2.8) of the CDF II detector, in 223  pb−1 of data. We measure σ×B=2796±13(stat)+95−90(syst)±162(lum)  pb. Combining this result with a previous CDF measurement obtained using electrons in the central region (|η|≲1), we present the first measurement of the ratio of central-electron to forward-electron W partial cross sections Rexp=0.925±0.006(stat)±0.032(syst), consistent with theoretical predictions using Coordinated Theoretical-Experimental Project on QCD (CTEQ) and Martin-Roberts-Stirling-Thorne (MRST) parton distribution functions.