That is the cover. The housing is the part which has the broken bolts.

Before you spend any time cleaning up the corrosion, remove the broken bolts. You might be needing the whole lower assembly if you can't get them out.

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“Whatever story you're telling, it will be more interesting if, at the end you add, "and then everything burst into flames.”
― Brian P. Cleary, You Oughta Know By Now