Midpoint rule/ttecniques of intergration numerical integration

Question

My Daughter has tried working this problem and looked at one similar and still can't get this right. Any help is appreciated.

Use midpoint rule with n-3 to approximate the integral integral of -3 to 4 (-9x+10x^2)dx

Answer 1

I just answered a similar problem and this one is perhaps a little less onerous.

Let f(x)=-9x+10x²

n=3 means 4 abscissas (values for x)

The abscissa values are -3, -2/3, 5/3 and 4

Calculate the midpoint of each interval.

Then calculate f(x) and each midpoint.

Add the 4 values of f(x) and multiply the sum by 7/3