If you are facing an issue wherein your Sharepoint users are having to download PDF files onto their local machines to view the files; the below post has got just the solution you are looking for.

Below Step by Step Powershell commands can be run to get the functionality working

From your Sharepoint Application Server; proceed to Start – All Programs – Microsoft Sharepoint 2010 Products – Sharepoint 2010 Management Shell and type below commands

$webApp = Get-SPWebApplication("http://yourwebapplicationurl")
$webApp.AllowedInlineDownloadedMimeTypes.Add("application/pdf")
$webApp.Update()

Once the above commands have been successfully run, you can confirm that the PDF application has been added to the MIME Type list using below command

$webApp.AllowedInlineDownloadedMimeTypes

The result is immediate and you can test the solution right away.