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Let $f : R \to R$ be defined as $f(x) = \begin{cases} 2\sin\left(-\dfrac{\pi x}{2}\right), & \text{if } x < -1 \ |ax^2 + x + b|, & \text{if } -1 \leq x \leq 1 \ \sin(\pi x), & \text{if } x > 1 \end{cases}$
If $f(x)$ is continuous on $\mathbb{R}$, then $a + b$ equals:
(1) 3
(2) $-1$
(3) $-3$
(4) 1
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