Let .Not sure if I am using this theorem correctly...

To evaluate x^2/(1+x^6) from negative infinity to positive infinity, I used x^2/x^6 as the comparison. After integrating, I took the limit from t to 0 as t -> - inf and the limit from 0 to s as s -> +inf of -1/(3x^3).

So, if I have done this much correctly, would the limit be convergent with them both equal to 0? Or divergent with them both equal to infinity?