Request feedback on basic integration concept
In my calculus text I have found something which is either a typo or a basic concept which I'm missing. I'd be grateful for opinions.
(By the way, this is not the first such question I've posted. It's not being pedantic; rather, I just want to ensure I'm not learning the wrong thing, or failing to learn the right thing. Because it is a high-selling, well-reviewed text ("Forgotten Calculus", by Barbara Lee Bleau)my first assumption is that I am wrong).
The relevant part of the question asks to find the integral of (1-x)^(2) dx.
But in the solution, the function to integrate is restated at the outset as (1- x^(2)) dx.
Based on my (admittedly novice) understanding of integration, these functions, and hence their integrals, are not the same.
For the integral of (1-x)^(2), I get
integral (1 - 2x + x^(2))
= x - x^2 + ((x^3)/3)
while for the integral of (1 - x^(2)) I get
x - (x^3)/3
Again -- am I right, or is there some reason that for the purposes of integration,
(1-x)^(2) = (1- x^(2)) ?