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For the first of these you'll use the integral from -2 to 1 of sqrt(x) - (x + 4) with respect to x. More generally, integral from a to b of the upper minus the lower function with respect to its input.
Just sketch the graphs and find the intersections of the two. The x values of the 2 intersections are your intervals. Then its just integral (with those intervals) of (the higher function - the lower function)