Assume that a function g(x) is continuous and non-negative in [a, b], and another function G(x) is also continuous in [a, b], where b> a. Is the additional condition G' (x) = g(x) for every x in (a, b) a necessary, sufficient, necessary and sufficient, or neither necessary nor sufficient condition for the area under the curve of g(x) over [c, d] to be given by G(d)-G(c) for all c, d where c = (a, b), de (a, b), and d > c? O Necessary and sufficient O Neither necessary nor sufficient O Sufficient, but not necessary O Necessary, but not sufficient O None of the above O No answer

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