Observe the roots, don't expand

Calculus Level 2

17(x1)(x7)dx= ? \large \int_{\color{#20A900}1}^{\color{#3D99F6}7} (x-\color{#20A900}1)(x-\color{#3D99F6}7) \, dx = \ \color{grey}?

Bonus: Can you generalize this for AB(xA)(xB) dx \displaystyle \int_A^B (x-A)(x-B) \ dx ?

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