"I Should Care" is composed by Axel Stordahl and Paul Weston and as a jazz standard has been recorded in thousands of versions by among other Frank Sinatra and Amy Winehouse.
Here's it's arranged for solo piano and played by Peter James on his album "Music for Ballet Class - MORE Songs from the 1940s".
It can be used in ballet classes for a jeté exercise.
For more info about the album click here: https://bit.ly/3uaJza1