What happens if we integrate, then differentiate?

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For a positive number \(a\), let \[I(a) = \int_0^a \! \left(4 - 2^{x^2} \right) \, dx.\]

Then \(\dfrac{dI}{da}=0\) when \(a\) equals

1. \(\dfrac{1 + \sqrt{5}}{2}\),

2. \(\sqrt{2}\),

3. \(\dfrac{\sqrt{5} - 1}{2}\),

4. \(1\).