ANTI-DIFFERENTIATION and DIFFERENTIATION
• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral. 
• The anti-derivative does not include "+c." The antiderivative of
is
not 
You mean the final answer doesn't have the +c included or?
It depends whether they ask for 'the' anti-derivative - which doesn't include the +c, or 'an' anti-derivative - which does.
I thought finding AN antiderivative means a specific antiderivative so you DON'T need the +c
Finding THE antiderivative means finding the FAMILY of antiderivatives so you NEED the +c
:X
Yup after checking Essentials text, I've confirmed the above to be correct.
There's a mistake in the following quote from the OP:
ANTI-DIFFERENTIATION and DIFFERENTIATION
• When anti-differentiating an indefinite integral, take care to include the “+ c” part. Along with the “dx” term immediately following the integral. 
• The anti-derivative does not include "+c." The antiderivative of
is
not 
AN = no +c
THE = NEED +c