It sounds like you have installed SQL Server 2005 Express Edition, which does not include SSIS or the Business Intelligence Development Studio.
BIDS is only provided with the (not free) Standard, Enterprise and Developer Editions.
EDIT
This information was correct for SQL Server 2005. Since SQL Server 2014, Developer Edition has been free. BIDS has been replaced by SQL Server Data Tools, a free plugin for Visual Studio (including the free Visual Studio Community Edition).