How to substract two Sums

Hi!

I've got two Sums vith variable arbitrary boundaries:

a:=Sum(x(i),i=n..m);
b:=Sum(x(i),i=n-1..m+1);

I would like to substract theese sums and I want Maple to simplify the result to

x(n-1)+x(m+1)

Is that possible?