Let's look for the parabola x^2+1 intersected by the line y = 10.

> plot([x^2+1,10],x=-5..5,color=[red,blue]);
>
>plot([x^2+1,10],x=-3..3,color=[red,blue]);

---

> egn:int(F(x),x=-3..3);

> F(x)=10-(x^2+1);

> egn:int(9-x^2,x=-3..3);

> plot([x^2+1,10,-3*x+1,3*x+1], x=-3..3,y=1..10);

> height=10-1;

> base=abs(-3)+abs(3);

> area:=1/2*height*base;

> area:=1/2*9*6;

> 4/3*area;

36

---

---