Let f: [a,b] -> R be continuous. Use Riemann's condition and uniform continuity of f to prove that f is integrable.
Usually it's a combination of:
1. Dumb luck at choosing the correct search string.
2. Sifting through the hits (which also means moving on to pages 2, 3 .....) until I find something I like.
Sometimes I'll have it saved as a favorite.
It's always nice to come across something new, interesting, different or comprehensive.