find the area under the curve
y = x^2 + x from the origin to the line x = 3
I will assume you want the area between the curve and the x-axis.
Under the curve would be infinitely large, it would be open below.
area = ∫ x^2 + x) dx from 0 to 3
= [(1/3)x^3 + (1/2)x^2 ] from 0 to 3
= 9 + 9/2 - 0 - 0
= 27/2 square units