integral simplifying

[lethalasian]

Original integral is Pi Integral [1,0] [(2-x)^2 - x]dx
After solving the integral
I got ((x-2)^3)/3 - (x^2)/2 from [1,0]
when simplifying i get (x^3)/3 -(5x^2)/2 + 4x - 8/3 from [1,0]
However, using the intergral-calculator.com and online solutions
it shows (x^3)/3 -(5x^2)/2 + 4x + C without the -8/3
This changes the answer I would get when plugging in the limits.
Am I missing something there?

 

[Dr.Peterson]

Changing the constant has no effect on the definite integral, since you would be subtracting it from itself.

Please show your work for evaluating from 0 to 1, so we can see why you think it matters.

Also, note that we read the limits of an integral from bottom to top, so rather than [1,0], you should be writing [0,1] as the interval over which the integral is taken.

 

[lethalasian]

thank you I got it! stupid multiplication error sorry
when plugging in the 1 to 5x^2 I squared the 5 instead of squaring the 1 then multiplying 5.