Under a parabola

Find an antiderivative and subtract its values at the endpoints.

1. An antiderivative of $x^2+2x$ is $F(x)=\frac{x^3}{3}+x^2$.
2. At the upper limit, $F(3)=\frac{27}{3}+9=18$.
3. At the lower limit, $F(0)=0$.
4. So the integral is $18-0=18$.

Answer: $18$