Like most others here, I have blindly gone for the complicated solutions
without thinking through the basics... sorry - I should have paid more
attention!

In reality, there is a simple solution to this problem, and it is just
this:

The reason you are not getting all of the dates including the 1st and last
day of the month is that you are using < and > when in fact it would be correct
to use <= and >= (less than OR equal to... greater than OR equal to).

Now, hopefully I've helped you (let me know if it works)... for now I'm
going to go sit in a corner and tremble.

:)