The area (in sq. units) of the region bounded by the parabola, y=x² + 2 and the lines, y=x+1, x=0 and x=3, is:

The correct option is B
Req. area = ∫₃₀(x² + 2)dx - ∫₃₀(x+1)dx
= [x³/3 + 2x]₃₀ - [x²/2 + x]₃₀
= (9 + 6) - (9/2 + 3)
= 15 - 15/2
= 15/2 = 7.5
This solution is incorrect. Let's try another approach.
The area is given by the integral:
∫₀³ [(x² + 2) - (x + 1)] dx = ∫₀³ (x² - x + 1) dx
= [x³/3 - x²/2 + x]₀³
= (3³/3 - 3²/2 + 3) - (0)
= 9 - 4.5 + 3
= 7.5 sq. units
The given options are integers. There must be a mistake in the question or the options. Let's reconsider the question.
Let's find the area between y = x² + 2 and y = x + 1 from x = 0 to x = 3.
Area = ∫₀³ [(x² + 2) - (x + 1)] dx
= ∫₀³ (x² - x + 1) dx
= [x³/3 - x²/2 + x]₀³
= 9 - 9/2 + 3 = 15/2 = 7.5
This is not among the options. There appears to be an error in the problem statement or the provided options.