Let X~UNIF(0,1) and Y~UNIF(0,1)

then I know that X+X~UNIF(0,2)

but how will X+Y be distributed?

Is there an easy way to determine this? I think it should be a triangle distribution of some sort.

If you look at the discrete uniform and think of 2 dice. If you throw the 2 dice there is 1 possible way to get 2. There are 2 ways to get 3. 3 ways to get 4 etc. up to 1 way to get 12. But how will this be adjusted for continuous uniform?