If f(x) and g(x) are continuous functions satisfying f(x) = f(a - x) and g(x) + g(a - x) = 2, then what is ∫[0 to a] f(x) g(x) dx equal to? - NDA Mathematics 2017 (I)

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If f(x) and g(x) are continuous functions satisfying f(x) = f(a – x) and g(x) + g(a – x) = 2, then what is ∫[0 to a] f(x) g(x) dx equal to?