Question

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

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

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

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

  4. \(1\).