This driver is version 126.96.36.19993, so it should be an improvement for you. There's an installer file within the .zip; if it fails to install, you can always try using Device Manager to install the driver.
i am aware of the auto driver check on hp's site as I said they haven't supported this laptop with any updates in a long long time
last graphics card update they put out was 2010
I highly doubt intel hasn't updated it since then the system developers don't tend to support products as long as the people who made those products
example had a gateway from the late 90s
windows updates no drivers
gateway support nothing posted on that model in over 2 years
the graphics card company had put out a new update less than 60 days ago