Actually you would want to use the Physics definition of average velocity. Physics states that average velocity is the change is position over the change in time.
You don't have to derive or integrate to find the answer to this problem. Derivation is necessary if you were to find the instantaneous velocity. We are not finding instantaneous velocity therefore no derivation is necessary.
Using the physics definition of Average velocity, you would do a (f(4)-f(1))/3
f(4) = 2(16)+6 = 38
38-5=33. Divide this by the change in time which is 3. Your answer should be 11. Thanks!