An integral membrane protein must have hydrophobic regions to interact with the hydrophobic cell membrane interior and hydrophilic regions for interaction with aqueous environments, thus the correct answer is C) Hydrophobic.
An integral membrane protein must possess hydrophobic regions to interact with the hydrophobic interior of the cell membrane. These proteins are amphipathic, meaning they have both hydrophilic and hydrophobic regions, allowing them to span the cell membrane so that part of the protein can interact with the cell's interior and part can interact with the extracellular environment.
The hydrophobic regions are important for anchoring the protein within the membrane, while the hydrophilic regions allow interaction with the aqueous environments on either side of the membrane.
Therefore, the characteristic that an integral membrane protein must possess is C) Hydrophobic. This is crucial for the protein to integrate into the lipid bilayer effectively and function in its role, whether that be as a receptor, ion channel, or another type of transmembrane protein.