Area under a Curve

Question 1
Increase the value of n using the slider. As the value of n increases, what can you say about the sum of the areas of the green rectangles, S, in relation to the area of the region bounded by the curve and the x-axis?
Question 2
Find the exact value of [math]\int_0^63x-\frac{1}{2}x^2dx,[/math] showing your working clearly.
Question 3
What can you say about the value of [math]\int_0^63x-\frac{1}{2}x^2dx[/math] in comparison to the area bounded between the curve y = 3x - 0.5x² and the x-axis?
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Information: Area under a Curve