Poisson process question and more...

Can anyone please help ...

Let $\displaystyle {X}(t)=\int_{0}^{t}\tau{d}{N}(\tau)$, where $\displaystyle {N}(\tau)$ is a Poisson process with rate $\displaystyle \lambda$.

Find $\displaystyle {E}{X}(t)$, and $\displaystyle cov\{{X}(t),{X}(\tau)\}$.

Also, let $\displaystyle {B}_{s}$ be Brownian motion and $\displaystyle {Y}(t)=\int_{0}^{t}({B}_{s}-{s})ds$,

Find $\displaystyle {E}{Y}(t)$, and $\displaystyle cov\{{Y}(t),{Y}(\tau)\}$.

I'm having real trouble with these, so if anyone could give concise details of steps involved with explanations, that would be great.