Doing sit-ups with your knees bent is more difficult.
Work Step by Step
As you use your core muscles to sit up, raising your torso and pivoting around your derriere, your legs tend to come off the floor, due to conservation of angular momentum (page 151-152). Gravity pulls down on your legs, providing a torque to fight this effect. Having your legs bent decreases the lever arm of the gravitational force, making it harder to keep your legs on the floor. Also, bending your legs gives them a smaller rotational inertia around the pivot point, maximizing their angular acceleration (which is not desirable for a sit-up where your legs should stay put).