We analyze air-exposed and cleaned graphene samples grown by the chemical vapor deposition method on polycrystalline copper. Raman spectra verify their single-layer nature. C 1s and C KVV Auger spectra confirm the dominant C sp2 coordination in the films. We use angular-resolved C 1s, O 1s, and Cu 3p photoelectron spectra to acquire non-destructive concentration depth profiles and for in-depth distribution of resolved bonding states by the Maximum Entropy Method. The elemental distributions show that the air-exposed surfaces of the samples are enriched by carbon-and oxygen-bearing species, resulting in an overlayer 0.6 nm in thickness. The in-depth distributions of the resolved bonding states reveal that the oxygen bonded to carbon is located at the top surface and the oxygen bonded to copper is located at the graphene/ copper interface. Almost no oxygen is present at the surface of the samples cleaned by annealing. The percentage of carbon falls by similar to 40%. The thickness of the carbon overlayer falls to about 0.3 nm, and the graphene layer completely covers the substrate. We emphasize that the results for the in-depth distribution of element concentrations and for resolved chemical bonding states are obtained nondestructively, i.e. without any modifications to surface composition and bonding.