Question

Investigating the bugs the two children
found on the playground and finding books to identify them instead of
doing your scheduled science lesson
for the day is an example of:
integrated learning or relevant learning
Would this be an example of relevant
learning?

Most likely since you did not do your scheduled science lesson this is mainly relevant learning. Hopefully, you integrate this into upcoming lessons (vocabulary words, ecology implications of bugs in science, math: plotting the frequency of finding bugs) to make an integrated lesson.

So when it has been cool, muggy, and downright dreary and suddenly the sun is shining outside, trot the kids outside for "relevant" learning....then integrate the outcomes and experiences into something educationally worthwhile.