There are many different definitions of arts integration in use, but I prefer and practice the most recent Kennedy Center definition:

Arts integration is an approach to teaching in which students construct and demonstrate their understanding through an art form.

Students engage in a creative process which connects an art form and another subject area, and meets evolving objectives in both.

For example, I find dance and science to be a natural fit with one another, since everything in the universe is in motion, and many science concepts lend themselves to choreography. Any cycle can be danced as a dance phrase, and students can create small group choreography about any concept that can be broken into component parts that contain motion.

My current arts integration workshops for teachers have titles like Scientific Thought in Motion, Poetry in Motion, Math on the Move, Active Algebra, & Classroom Choreography.