That is, the variable of integration is a “dummy variable” in the sense that any other variable produces the same result.

For example, 



That is, interchanging the limits of integration changes the integral’s

For example,   



That is the interval over which a definite integral is to be evaluated may be subdivided.

For example, you may verify that



4.  Geometrically, can be interpreted as the area of the region bounded by the curve y = f(x), the x-axis and the lines x = a and x = b.


Similarly, can be interpreted as the area of the region bounded by the curve x = g(y), the y-axis and the lines y = c and y = d.


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