The smallest value of \[I(a) = \displaystyle\int_0^1 \! (x^2 - a)^2 \, \mathrm{d}x,\] as \(a\) varies, is…

The orange curve here is \(y = (x^2-a)^2\), while the white region is \(I(a)\)

The orange curve here is \(y = (x^2-a)^2\), while the white region is \(I(a)\)