The first term is a constant and you can call it whatever you want.
From the start point of
integrating between and produces the result
If the coefficients are calculated (by multiplying both sides by and integrating betwen and ), you find that the fraction in front of each integral is .
So, you have a choice. Either leave things as they are in which case one of the integrals has at the front and the others have . Or, call the constant , in which case the 2's cancel and you have the consistency of all of the integrals having at the front.
Some choose the first option others choose the second.