Answer
Within 0 to 15 weeks the honeybee population has increased and that amount is added to the initial population of 100 honeybees.
Work Step by Step
We know that the population starts with 100 bees and that 100 is added to the integral it’s not a part of it so the initial amount before the integral is 100. So within the context of the question the population starts with an initial 100 bees.
The rate we are given for n’(t) is bees per week and so the integral result should give us a unit of bees and the b and a of the integral should represent weeks.
B= 15 weeks
A = 0 weeks
So the rest is a matter of putting all the go together and you got your answer.