Answer:
a)

b) P(2) = 14 units
c) from hour 4 to hour 5, an average worker can complete about 0.1 of a unit.
Explanation:
Notice that the problem gives the derivative of the production function, and also an extra piece of information (P(2) = 14) - also called initial condition - that allows us to find the actual production with any additional constant.
Let's work on the "antiderivative" of the function:

Using the change of variables
,
becomes

Then, the family of antiderivatives becomes:

We should be able to determine the constant C using the initial condition for the problem:

Then we evaluate:

Then the function requested in point a) is:

Point b) "Find the number of units an average worker can complete 2 hours after beginning work" was already given as the initial condition, so P(2) = 14 units.
Point c) asks for the number of units an average worker can complete from hour 4 to hour 5, so we calculate the difference:

So the average worker can complete one tenths of a unit between hour 4 and hour 5.