FX = x ^ 2-2x + 2, X ∈ [T, t + 1], t ∈ R, find the expression of the minimum value g (T) of function FX

When 1 ∈ [T, t + 1], when - 1 ″ t ″ 1, f (1) is the minimum, it is 1
When t > 1, the function is an increasing function, G (T) = f (T) = T ^ 2-2t + 2
When t

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1. Let f (x) = x2-2x + 2, the minimum value of X ∈ [T, t + 1] (t ∈ R) be g (T), and find the expression of G (T)
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