see the attached figure to better understand the problem
we know that
the estimate of the area under the curve is equal to
[tex]Area\ estimate=Area\ of\ the\ complete\ rectangle-(Area\ triangle1\ +\ Area\ triangle 2)[/tex]
[tex]Area\ of\ the\ complete\ rectangle=4*6=24\ units^{2}[/tex]
[tex]Area\ triangle1=\frac{1}{2} (1.5*3)=2.25\ units^{2}[/tex]
[tex]Area\ triangle2=\frac{1}{2} (2.5*5)=6.25\ units^{2}[/tex]
substitute the values
[tex]Area\ estimate=24\ units^{2}-(2.25\ units^{2}+6.25\ units^{2})[/tex]
[tex]Area\ estimate=15.5\ units^{2}[/tex]
therefore
the answer is
[tex]15\ units^{2}[/tex]
