Question 1119908
You didn't give limits so I'll make my own.
You can modify the solution as needed.
*[illustration dfp1.JPG].
So find the area between {{{x=-1}}} and {{{x=0}}}.
The four regions are from
{{{x=-1}}} to {{{x=-0.75}}}
{{{x[M1]=-0.875}}}
{{{x=-0.75}}} to {{{x=-0.5}}}
{{{x[M2]=-0.625}}}
{{{x=-0.5}}} to {{{x=-0.25}}}
{{{x[M3]=-0.375}}}
{{{x=-0.25}}} to {{{x=0}}}
{{{x[M4]=-0.125}}}
Find the difference of the functions at the midpoints,
{{{D=-x-(-x^3)=x^3-x}}}
So,
{{{D[1]=(-0.875)^3+0.875=0.205078}}}
{{{D[2]=(-0.625)^3+0.625=0.380859}}}
{{{D[3]=(-0.375)^3+0.375=0.322266}}}
{{{D[4]=(-0.125)^3+0.125=0.123047}}}
Sum the differences and multiply by the step in x {{{0.25}}},
{{{A[4]=(0.205078+0.380859+0.322266+0.123047)0.25}}}
{{{A[4]=1.03125(0.25)}}}
{{{A[4]=0.257}}}