JEE Math Practice Question

Let $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be a function defined as $$f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x], a \in \mathbb{R}$$ where $$[t]$$ is the greatest integer less than or equal to $$t$$. If $$\mathop {\lim }\limits_{x \to -1 } f(x)$$ exists, then the value of $$\int\limits_{0}^{4} f(x) d x$$ is equal to

1. A.$$-$$1
2. B.$$-$$2
3. C.1
4. D.2