Start drawing vertical lines.
At x = 0, G(x) = 0
As x increases from x = 0, you get trapeziods. One parallel length obviously is 10. The other is obtained from the equation of the line between (0,-10) and (10,-20). Calculate the area of ALL such trapezoids, depending on the value of x.
Of course, this piece will be negative.
Do the same with the next line segment, starting where the last piece left off.