It's a method based on the product rule of differentiation
Okay, let's take a general example :
The integrating factor is defined as (it is not necessary to have boundaries)
Why is it useful ? Because the product rule will help you eliminate y'.
We indeed have, after multiplying by the integrating factor :
But look at the LHS.
You can see (or you know) that it's the derivative of
---> apply the product rule (along with the chain rule) to check this :
So finally, becomes :
And in order to get y, integrate both sides of the equation. And then divide by
In this case, it's "easy", because p(x)=1. And thus the integrating factor is
Am I speakig Chinese to you ?
Anyway, you can find lots of reference in google, looking for "integrating factor"
Bad Chinese perhaps...
So far you seem to be indicating that you do not know the product rule for derivatives (google for "product rule calculus"), and are not at home with functional notation. If so I doubt we can help you, go back to your instructor and ask for help.