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The Upsilon production cross section in proton-proton collisions at sqrt(s) = 7 TeV is measured using a data sample collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 3.1 +/- 0.3 inverse picobarns. Integrated over the rapidity range |y|<2, we find the product of the Upsilon(1S) production cross section and branching fraction to dimuons to be sigma(pp to Upsilon(1S) X) B(Upsilon(1S) to mu+ mu-) = 7.37 +/- 0.13^{+0.61}_{-0.42}\pm 0.81 nb, where the first uncertainty is statistical, the second is systematic, and the third is associated with the estimation of the integrated luminosity of the data sample. This cross section is obtained assuming unpolarized Upsilon(1S) production. If the Upsilon(1S) production polarization is fully transverse or fully longitudinal the cross section changes by about 20%. We also report the measurement of the Upsilon(1S), Upsilon(2S), and Upsilon(3S) differential cross sections as a function of transverse momentum and rapidity.