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The area of the region $A = {(x, y) : 0 \leq y \leq x|x| + 1$ and $-1 \leq x \leq 1}$ in sq. units is:
(1) $\frac{2}{3}$
(2) 2
(3) $\frac{4}{3}$
(4) $\frac{1}{3}$
Area $= \int_{-1}^{0}(-x^2+1),dx + \int_0^1 (x^2+1),dx = \frac{2}{3} + \frac{4}{3} = 2$.
BETA
