Let the functions f: R ⟶ R and g: R ⟶ R be defined by f(x) = e^(x−1) − e^(−|x−1|) and g(x) = ....

This is the Solution of question from JEE Advanced 2020 Paper 1 question of mathematics.
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Let the functions f: R ⟶ R and g: R ⟶ R be defined by
f(x) = e^(x−1) − e^(−|x−1|) and g(x) =1/2(e^(x−1) + e^(1−x)).

Then the area of the region in the first quadrant bounded by the curves y = f(x), y = g(x) and x = 0 is
(A) (2 − √3) + 1/2(e − e^(−1))
(B) (2 + √3) + 1/2(e − e^(−1))
(C) (2 − √3) + 1/2(e + e^(−1))
(D) (2 + √3) + 1/2(e + e^(−1))

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[kundankumarsinha]

Thank you sir for the great explanation ❤️