stochastic calculus - Integral of Brownian motion w.r.t. time

Let

$$X_t = \int_0^t W_s \,\mathrm d s$$

where $W_s$ is our usual Brownian motion. My questions are the following:

1. Expectation?


2. Variance?


3. Is it a martingale?


4. Is it an Ito process or a Riemann integral?

Any reference for practicing tricky problems like this?

For the expectation, I know it's zero via Fubini. We can put the expectation inside the integral. Now, for the variance and the martingale questions, do we have any tricks? Thanks!