Update R using RStudio
You install a new version of R from the official website.
RStudio should automatically start with the new version when you relaunch it.
In case you need to do it manually, in RStudio, go to :Tools -> options -> General.
Check @micstr's answer for a more detailed walkthrough.
How to upgrade RStudio version?
RStudio is an application (specifically, an Integrated Development Environment, or IDE). This is a common tool for using R, which is a computer language. Much like Microsoft Word is a common tool for writing documents in English (or other languages - and in fact you can use RStudio to write files other languages like RMarkdown, Python, SQL, French, or Swahili.). However, just like you can write English in programs other than Word, you can also write and run R code in programs other than RStudio.
You can find the most recent version on the RStudio website, or you can look in the Help
menu and select "Check for updates", which will give you a download link if a newer version is available.
Given the version number you show, 3.4.0, you need to upgrade R (the language), not RStudio (the application). The current RStudio version as I write this is 1.3.*, while the current R version is 4.0.*.
The place you need to go to update R is CRAN - their website has download links for Windows, Mac, and Linux.
R Update | Version mismatch
In RStudio, go to Tools ... Global Options ... General ... Basic .. R Sessions. It allows you to choose a specific version of R
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