Integral going through zero - don't understand calculator answer

[medicalphysicsguy]

I am trying to understand why for the function

(1-x^2)dx,

integrating from -2 to -1 gives -4/3,
integrating from -1 to 1 gives 4/3

but integrating from -2 to 1 gives, according to the online integral calculator, -8.3267 .

I get zero for this integration, though I can see how one might want to partition the curve into two and take the absolute value of each for a total of 8/3 in some applications.

Would anyone be able to explain why the integral calculator is giving -8.3267 . Many thanks!

 

[pka]

I am trying to understand why for the function (1-x^2)dx,
I get zero for this integration, though I can see how one might want to partition the curve into two and take the absolute value of each for a total of 8/3 in some applications.
Would anyone be able to explain why the integral calculator is giving -8.3267 . Many thanks!

\(\displaystyle \left. {x - \frac{1}{3}x^3 } \right|_{ - 2}^1 = \left( {1 - \frac{1}{3}} \right) - \left( { - 2 + \frac{8}{3}} \right) = 0\)