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

\(\frac{3}{20}\),

\(\frac{4}{45}\),

\(\frac{7}{13}\),

\(1\).

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

\(\frac{3}{20}\),

\(\frac{4}{45}\),

\(\frac{7}{13}\),

\(1\).