Final answer:
The sartorius muscle is the only muscle innervated by the femoral nerve in the anterior thigh compartment that does not do extension.
Step-by-step explanation:
The only muscle innervated by the femoral nerve in the anterior thigh compartment that does not do extension is the sartorius muscle. The sartorius muscle is a long, thin muscle that runs diagonally across the thigh and is responsible for flexing, abducting, and laterally rotating the leg at the hip.