Cook the whole wheat pasta according to package instructions until al dente. Drain and rinse under cold water to cool.
In a large bowl, combine the cooked pasta, arugula, cherry tomatoes, cucumber, red onion, and feta cheese.
In a small bowl, whisk together the olive oil, lemon juice, Dijon mustard, salt, pepper, and red pepper flakes (if using).
Pour the dressing over the pasta salad and toss gently to combine all ingredients.
Taste and adjust seasoning if necessary. Chill in the refrigerator for at least 30 minutes before serving to allow flavors to meld.
Serve cold or at room temperature.