This integral can be split up into the sum of two integrals (Property 4, p. 331):
Let's graph these functions separately and try to evaluate their integrals by looking at the areas under the graphs.
This region has the same amount of area above the x axis as it does below the x axis, so these areas cancel each other out, and the value of the integral is zero.
This region is a triangle of base 2π, height 10π. Its area is