Use the method of quadrature to estimate the area under the curve y=-x^2+5 and above the x-axis from x=0 to x=2.

I'm a calculus teacher at the high school level and I have never heard of quadrature.  I teach from an AP approved college-level text so...I'll do it using the antiderivative!  Setting that up to integrate we have .  If you notice, I pulled the negative out in front of the integral and changed the signs in the function.  So it could really be rewritten as .  Integrating we have from 0 to 2.  Subbing in those bounds, we have which simplifies to .  Distributing the -1 in gives us