Reversal of nested integrals

I am suppose to reverse the order of integration and then evaluate the following integral.

integral from 0 to 1 of the integral from y^(1/2) to 1 of (2 + x^3)^(1/2) dx dy

When I do this I end up with the square root of x to 1 for the bounds and have no value to plug in for the square root of x!!!!! I know I am doing something wrong.

I am getting integral from x^(1/2) to 1 of integral from 0 to 1 of (2 + x^3)^(1/2) dy dx

which becomes

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

but then I have 2/3(2 + x^5) -- 2^(1/2)x evaluated from x^(1/2) to one. But alas, I have no value to plug in for the square root of x!!!! Can someone tell me where I have gone wrong??? Thanks for looking at this. Frostking

Nested integral bounds question

Thanks so much for your assistance. I was able to evaluate the integral just fine with your help but I am afraid I do not understand how you obtained 0 and x^2 as bounds for the inner integral. Frostking