Reverse the order of integration

I'm not sure I follow the concept of reversing the integral. Why do I need to reverse it?
And how would I do that? For example, if I have the double integral of
∫(from 0 to 1) ∫(from sqrt(y) to 1) sqrt(2 + x^3) dxdy, what would the reverse integral be?

it's because you can't integrate sqrt(2 + x^3) with respect to x first. This is non-elementary integral.

you need to draw your region to see reverse process.
The region is the area under y = x^2, and x ranges from 0 to 1.

so ∫∫ sqrt(2 + x^3) dy dx, y = 0 to x^2, and x = 0 to 1.

integrate with respect to y first,
y sqrt(2 + x^3)

evaluating the limits
x^2 sqrt(2+x^3)

now integrate with respect to x
(2/9) (2+x^3)^(3/2)

evaluating the limits
(2/9) (3^(3/2) - 2^(3/2))

or
(2/9) (sqrt(27) - sqrt(8))

Whats your major lol lets be homework buddies ok.