This differential equation came up in a problem I'm working on. I've never seen one with the function or its inverse in a limit of integration. Can anyone point me in the right direction (or maybe even show me how to solve it)? Thanks.

$y^{\prime }(x)[1-x]^{2}x-\int_{y^{-1}(x)}^{x}(y(z)-x)2zdz=0$

Initial condition: $y(1) = 1$