For Karyn Parsons, storytelling has always been in her blood – even during her days playing the charmingly highfalutin Hilary Banks, older cousin of Will Smith, on the TV series “The Fresh Prince of Bel-Air,” and living in glossy Los Angeles as a successful 20-something actress. It was her craving for tales of tenacious protagonists that led Ms. Parsons to create Sweet Blackberry, a children’s film production company dedicated to telling the unfamiliar but true stories of black Americans and bringing them to life through animation. “Things that are really painful in history, in African-American history, I think a lot of people just shut [them] out,” Parsons says while talking over cups of Earl Grey tea.

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