Definite integrals and their properties

There are some interesting properties of definite integrals worth noting, and it is perhaps necessary to further amplify the remarks on page 232. 

A definite integral is a fimction of its limits. If f (x) denotes the first differential coefficient of f(x), 

This means that a definite integral is a function of its limits, not of the variable of integration, or 

In other. words, functions of the same form, when integrated between the same limits have the same value. 

The interchange of the limits of a definite integral causes the integral to change its sign. It is evident that 

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