I was asked to define the next intergrals and I want to know if I did it right:  

$$1) \int^\infty\_a f(x)dx = \lim\_{b \to \infty}\int^b\_af(x)dx$$
$$2) \int^b\_{-\infty} f(x)dx = \lim\_{a \to -\infty}\int^b\_af(x)dx$$
$$3) \int^\infty\_{-\infty} f(x)dx = \lim\_{b \to \infty}\int^b\_0f(x)dx + \lim\_{a \to -\infty}\int^0\_af(x)dx$$
Thanks.