¿Cómo configuro mediante programación la cadena de conexión para Entity-Framework Code-First?

debe usar el EntityConnectionStringBuilder clase

string providerName = "System.Data.SqlClient";
string serverName = ".";
string databaseName = "AdventureWorks";

// Initialize the connection string builder for the
// underlying provider.
SqlConnectionStringBuilder sqlBuilder =
new SqlConnectionStringBuilder();

// Set the properties for the data source.
sqlBuilder.DataSource = serverName;
sqlBuilder.InitialCatalog = databaseName;
sqlBuilder.IntegratedSecurity = true;

// Build the SqlConnection connection string.
string providerString = sqlBuilder.ToString();

// Initialize the EntityConnectionStringBuilder.
EntityConnectionStringBuilder entityBuilder =
new EntityConnectionStringBuilder();

//Set the provider name.
entityBuilder.Provider = providerName;

// Set the provider-specific connection string.
entityBuilder.ProviderConnectionString = providerString;

// Set the Metadata location.
entityBuilder.Metadata = @"res://*/AdventureWorksModel.csdl|
                        res://*/AdventureWorksModel.ssdl|
                        res://*/AdventureWorksModel.msl";
Console.WriteLine(entityBuilder.ToString());

using (EntityConnection conn =
new EntityConnection(entityBuilder.ToString()))
{
conn.Open();
Console.WriteLine("Just testing the connection.");
conn.Close();
}