You should write your IVP this way:
Then you can see that your IF is off by a sign. Once you get the IF, what you do is multiply the entire DE by the IF (makes sense, since it is called an integrating factor, after all!). The LHS should then be the derivative of a product, which you can integrate directly. The RHS will still just have t's in it - no y's. So you can integrate that side as well.