Area Between Line and Parabola

(1) Calculate the INTEGRAL of (x+1)-(x² - 5) between x= -2 and x = 3, and show that the area displayed is correct.
(2) Move the line until it intersects the curve at (-1,-4) and (2,-1). Observe the area and calculate an integral to confirm it.
(3) Move the line until it is TANGENT to the curve - then A and B are the same point. Then the area is zero. Where is the tangent point?
(4) Find a position for the line where the area is as close as possible to 7. Use calculus to find the EXACT position of the line.

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Dave Mulkey, Created with GeoGebra