Fundamental theorem of calculus proof

Then from the definition of A(x):

This represents the area of the region under the graph of f and over the horizontal axis, bounded on the left by the vertical line t = a and on the right by the vertical line t = x + h, as shown in the diagram below.

Area under graph represents A(x + h)

Likewise,

represents the area of a similar region, but bounded on the right by the vertical line t = x as shown in the next diagram.

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