নির্দিষ্ট যোগজের বৈশিষ্ট্যসমূহের সারসংক্ষেপ

If a function $f$ is positive, then the definite integral $\int_a^b f(x)\ dx$ can be interpreted as the area under the graph $y = f(x)$, above the $x$-axis, and between $x = a$ and $x = b$.

This leads to the following properties, which are also true for integrable functions in general:

$$\int_a^a f(x)\ dx = 0$$

(This is the area of a vertical line segment of zero width.)

$$\int_a^b f(x)\ dx + \int_b^c f(x)\ dx = \int_a^c f(x)\ dx$$

(Here, we are adding the two adjacent areas, and expressing the result as one definite integral.)