I'd stay away from differential as well. When dealing with functions, the differential measures the changes in the linear nature of functions.
I think that strongm's suggestion of 'Riemann Integral' makes the most sense since that's the formula used to calculate the area under the curve. Just as
[π]r2 = Area of a circle with radius r
[∫]ab f(x) dx = Area under the curve created by the function f(x) from point a to point b. That is a Reimann Integral.
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