intergration with partial fractions

I am doing this problem:

integral of (x^3 + x - 1)/((X^2 +1))^2 dx

So i set that integral equal to (Ax + B)/(x^2 + 1) + (Cx + D)/((x^2 + 1))^2

I got ax^3 + ax + bx^2 + b + cx + d = 1x^3 + 1x - 1

so..

x^3 terms: a = 1

x^2 terms: b = 0

x^1 terms: a + c = 1 ( c = 0)

x^0 terms: b + d = -1 ( d = -1)

I put these back into the equation and got

integral of 1/(x^2 + 1) + integral of -1/((x^2 + 1))^2

which equals ln(x^2 + 1) + 1/(x^2 + 1) + C

The answer in the book has those 2 first terms as the answer..but has 2 more terms, then the Constant..I am having trouble finding the correct answer. What did I do wrong?