Question

The graph of f consists of line segments, as
shown in the figure. Evaluate each definite integral by using geometric formulas.
See attached.

Answer 1

from 0 to 1 you have a triangle lying below the \(x\) axis
the base is 1, the height is also 1, and so the area of that little triangle is
\[\frac{1}{2}\]
therefore
\[\int_0^1f(x)dx=-\frac{1}{2}\] and so
\[-\int_0^1f(x)dx=\frac{1}{2}\]

Answer 2

others are similar

Answer 3

I think I understand