Aus Online Mathematik Brückenkurs 2

The value of the integral can be interpreted as the area under the graph \displaystyle y=2 from \displaystyle x=-1\ to \displaystyle x=2.

Because the region is a rectangle, we can determine its area directly and obtain

\displaystyle \int\limits_{-1}^{2} 2\,dx = \text{(base)}\cdot\text{(height)} = 3\cdot 2 = 6\,\textrm{.}