This is a partner question to How do centaurs get enough oxygen to run
Centaurs are a common mythological figure, with the body of a man where a horses head would be. They usual exist in a fantasy world but lets say they are not sustained by magic but instead by biological processes.
This has obvious advantages in terms of speed, maneuverability, visibility, etc. There is however one obvious problem, they have the small mouth and throat of a human trying to support the energy and oxygen requirements of the massive body of both a human and a horse.
Humans are not adapted to eat grass or grains, however a centaur could potentially have a horse's digestive system so would centaurs be able to live on grass? If they could would they be able to graze? It seems their body shape would be more suited to giraffe-like eating fruit and leaves from trees rather than grazing of grass.
Could they get enough energy that way though given their smaller mouth? Would they need to be carnivorous or at least omnivorous?