When you open a PDF file in SharePoint 2010, it tends to ask for saving the file on the local drive. Follow the following steps to make it open the PDF files within the browser.
1- Open SharePoint Central Administration.
2- Click on Web Application Management.
3- Highlight the Web Application you want (usually the main site collection on port 80).
4- Click on General Settings.
5- In the Browser File Handling section, choose Permissive.