Integrate the given series expansion of `f`  term-by-term from zero to `x`  to obtain the corresponding series expansion for the indefinite integral of `f`.

`f(x) = (-2 x)/(1+x^2)^2 = sum_(n=0)^(oo) (-1)^n 2 n x^(2 n - 1)`

`int_0^x f(t) dt = sum_(n=1)^(oo)`  

Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question