Definite Integral, FTC: int[0,1] [(t - t^2)^2] dt

[cmnalo]

∫(t-t^2)^2dt interval(0,1)

u= t-t^2
du = 1-2tdt
dt = du /1-2t

∫(u)^2dt

∫ (u)^2 (du/1-2t)

I'm having trouble with the next step. U^2 would become 1/3(u)^3 but how do I deal with the du/1-2t?

 

[skeeter]

you can't do this definite integral using substitution.

expand (t - t²)², then integrate.