Final answer:
The two types of integral transmembrane proteins are channel proteins, which allow the passage of specific molecules, and carrier proteins, that change shape to transport molecules across the membrane.
Step-by-step explanation:
The two types of integral transmembrane proteins are channel proteins and carrier proteins. Channel proteins create hydrophilic pathways that allow certain molecules, such as ions and water (aquaporins being a prime example), to pass directly through the membrane following their concentration gradient. Carrier proteins, on the other hand, bind to the molecules they transport, often changing shape to shuttle these molecules across the membrane; this process can be either passive or active, depending on whether it requires energy input.