Bring a large pot of lightly salted water to a boil. Add the rigatoni and boil 8 minutes, or until firm/tender, with some resistance to the bite. While the pasta cooks, place the pasta sauce in a large skillet and bring to a simmer over medium heat. When the pasta is firm/tender, add the broccoli to the pot and cook 2 minutes more, or until the pasta and broccoli are tender. Drain, reserving 1/2 cup of the cooking liquid. Place the drained pasta and broccoli and the reserved cooking liquid in a large serving bowl. Add the pasta sauce and cheese, toss to combine and serve.