We first note that on the interval0 x 14the function is sometimes above the x-axis and sometimes below the x-axis. Therefore, we must apply the following property wherea < c < b.cag(x) dx +bcg(x) dx =bag(x) dxThere are three distinct intervals fromx =0tox =14,where the function moves from one side of the x-axis to the other. These intervals are0 x 4,4 x 12,and12 x 14.Therefore, applying the rule above gives us the following result.140g(x) dx =0g(x) dx +4g(x) dx +12g(x) dx