Accounting for restricted x-values in fractional (linear/linear) derivatives

Hello everyone,

I was working on a problem (solution shown):

http://www4d.wolframalpha.com/Calcul...=57&w=344&h=37

and checking my work with wolfram alpha to find that there is a "restricted x-value" constant that is added in to the end of the integral, in this case 4/9. I don't know how this value was calculated, but Wolfram has the steps it took here: http://www.wolframalpha.com/input/po...e46hi91b8&s=57

Could someone possibly explain the use of this constant and how it was calculated, since it can be eliminated anyway if C=-4/9?

Also, are there other cases when this need be calculated? Could you point me to some places where I can get some practice?

Help is greatly appreciated!