If and are any two antiderivatives of the same function on an interval

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

If F(x)F(x) and G(x)G(x) are any two antiderivatives of the same function f(x)f(x) on an interval II, which of the following is ALWAYS true on II? (a) F(x)−G(x)F(x)-G(x) is a constant (b) F(x) G(x)F(x)\,G(x) is a constant (c) F(x)G(x)\dfrac{F(x)}{G(x)} is a constant (d) F(x)+G(x)F(x)+G(x) is a constant

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