Question: Consider now the function A(x) defined as the area under the graph of f(t) for a t x, as in Figure 3.

Figure 3 : Area under the graph of f(x)

Use Part b to argue that, for every h > 0 and every x > a, there is t _h such that

A(x+h) – A(x) = f (t _h )h. (14)

Hint: Notice that A(x + h) – A (x) is that area represented in Figure 4.

Figure 4 : A(x + h) – A (x)

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