# <Solved>When to use the F(b)-F(a) formula in definite integrals?

#### Elena Baby

I'm trying to solve this formula:
$image=https://latex.codecogs.com/gif.latex?%5Cint_%7B-1%7D%5E%7B1%7Dx-1/%283%5Ex+3%5E%7B-1%7D%29dx&hash=d09794486d6dcb5b1b5c6a35c1ea4ff8$

I wrote this:
F(1)-F(-1)=0-2/1/(3+3)=-3/5
But then I was told I should split the formula.I know it makes the solution easier because
$image=https://latex.codecogs.com/gif.latex?%5Cint_%7B-1%7D%5E%7B1%7D-x/%283%5Ex+3%5E%7B-1%7D%29dx&hash=a2a92c581b358dc6be30017de99c8e36$
is odd.But I don't see why it's necessary.
Why is that?
And the other half is written as:
$image=https://latex.codecogs.com/gif.latex?%5Cint_%7B-1%7D%5E%7B1%7D1/%283%5Ex+3%5E%7B-1%7D%29dx&hash=a631949a43b38f410a19c9570d3d6146$

Why can't we write:F(1)-F(-1)=0 ?
What function were you using for F($x$)? I can suggest a suitable function if you wish, as you don't seem to have found one. If you found your mistake, we'd still like to check your work for you, now that you've posted the integral.