1. Let \(c\) be a real number and define the following integral \[I(c) = \int^1_0 2^{-(x-c)^2} dx.\]

State the value(s) of \(c\) for which \(I(c)\) is largest. Briefly explain your reasoning. [Note you are not being asked to calculate this maximum value.]

The curve here is \(y = 2^{-(x-c)^2}\), and the white region is \(I(c)\).

Before moving the slider, what effect will it have on the curve?

When will \(I(c)\) have its largest value?