tsql add primary key column on existing table

I can add a new column to an existing table no problem, but i had problem making it an autoincrement int primary key. After some research I found the solution: "Identity" keyword:

if not exists(SELECT * FROM INFORMATION_SCHEMA.COLUMNS WHERE TABLE_NAME = 'table1' AND COLUMN_NAME = 'ID')
begin

    ALTER TABLE dbo.table1
    add ID int identity not null
       
end
go