Is it possible to use three screens with Intel HD 3000 integrated graphics?

No, according to Intel's FAQ on the HD 3000 integrated graphics:

No. Intel® graphics products can output to one or two display devices at the same time. More than two display devices can be physically connected, but only two display devices can be used at any time.

However it seems you can use a splitter to "clone" a third monitor.

Some customers report being able to use third-party video splitter devices to allow output to more than two display devices. Intel has not tested these configurations nor can make recommendations on these third party devices.

Keep in mind cloning only mirrors exactly what is on one of the two monitors it will not be an independent third monitor.

As already answered you just have 2 concurrent outputs. But you can split it (it's not mirroring).

So you take a big resolution (e.g. 3200x1200) and split it into two (e.g. 2x 1600x1200). You need to have these resolutions (there are some possibilities). I done it years ago with triple split (1 output to 3 monitors) for creating a cave with one graphics card.