URGENT!! Calculate double Integrals

Calculate the double integral of:
((xy^2) / (x^2+1))dA, R={(x,y)| 0

Need to find the value of the integral _____________________

Please show all steps. Thanks for the help in advance!!

∫(x = 0 to 3) ∫(y = -1 to 1) (xy^2 / (x^2 + 1)) dy dx
= ∫(x = 0 to 3) x dx/(x^2 + 1) * ∫(y = -1 to 1) y^2 dy
= [(1/2) ln(x^2 + 1) {for x = 0 to 3}] * [(1/3) y^3 {for y = -1 to 1}]
= [(1/2) ln 10 - 0] * [(1/3) (1 - (-1))]
= (1/3) ln 10.

I hope this helps!