You are tracking the velocity and position of a rocket-propelled object near the surface of Mars. The velocity is v(t) and the position is s(t), where t is measured in seconds, s in meters, and v in meters per second. It is known that the v(t) = ds/dt = 4.94 - 3.72t and s(0) = 5.

A.Explain why the condition "f is continuous over [a, b]" from the Evaluation Theorem is fulfilled by this scenario.

B.Explain why the condition "F is any antiderivative of f on [a, b]" from the Evaluation Theorem is fulfilled by this scenario.

C.Determine the position function s(t) using the initial condition that s(0) = 5.

D.Apply the Evaluation Theorem to this scenario to compute v(t)dt 3 1 .

E.Explain why solving the rocket's displacement in meters over the time interval from t = 1 to t = 3 is an application of the evaluation theorem.