Sub-part i and ii
For graphing I suggest you use Desmos Online Graphing Calculator. By graphing these two equations you can visualize the bounded area and note that y2 = x + 5 is the top bound of the area and y1 = 2x2 + 2 is the bottom bound.
To solve for the intersection points of two lines simply set the two equations equal to one another and solve.
2x2 + 2 = x + 5
2x2 - x - 3 = 0
(2x - 3)(x+1) = 0
The two lines would thus intersect at x = 3/2 and x = -1. Use the graph to verify that this is correct.
To solve for the area between two curves use the formula
∫ab f(x) - g(x) dx
where f(x) is the top bound of the area, g(x) is the bottom bound of the area, and [a,b] is the interval over which we are solving for the area.
In this case we know f(x) = x + 5, g(x) = 2x2 + 2, and [a,b] = [-1, 3/2] so
∫-11.5 x + 5 - (2x2 + 2) dx
∫-11.5 x + 5 - 2x2 - 2 dx = 5.20833
I hope this helps! If you have any questions let me know.
Best of luck,