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Question:

The area of the region A = [(x,y): 0 ≤ y ≤ x|x| + 1 and -1 ≤ x ≤ 1] in sq. units is:

23

2

43

13

Solution:

The graph is as follows:
∫₋₁⁰(-x² + 1)dx + ∫₀¹(x² + 1)dx = 2