APFIVE Definite Integral of a Piecewise Function
Let $$f$$ be the function defined by $$f(x) = \begin{cases} x^2 & \text{for } x < 0 \\ -1 & \text{for } x = 0 \\ x & \text{for } x > 0 \end{cases}$$. What is the value of $$\displaystyle \int_{-1}^{1} f(x) \, dx$$?
A
$$\displaystyle \frac{5}{6}$$
B
$$\displaystyle -\frac{1}{6}$$
C
$$\displaystyle \frac{2}{3}$$
D
nonexistent
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