Use the Midpoint Rule to approximate the integral (5x-9x^2)dx from 6 to 15
That is also known as the trapezoidal rule. Evaluate the funtion at 6,9,12 and 15. That is a gap of h=3 between points. You could use smaller intervals but that should be good enough.
The approximation to the integral will be:
h[(1/2*f(6) + f(9) + f(12) + (1/2)*f(15)]
= 3*[-147 -831 -1236 -1050]
where f(x) is the 5x-9x^2 function.
I tried comparing that to exact value. It is not very close. It would be better to calculate the approximation with h = 1, with numerical entries at 6,7,8,...15.