Is "I must to finish my homework" correct?

Why

Vivaan has correctly noticed a real pattern — many verbs in English genuinely do connect to a second verb using "to", exactly as in "I want to finish" or "I need to go". Modal verbs, though — must, can, will, should, might, and others — belong to their own special category that behaves differently: they connect directly to the plain base form of the next verb, with no "to" in between at all. "Must to finish" inserts a connector that modals simply never use, unlike ordinary verbs such as "want" or "need". Test: run through several modals the same way — "I can to swim", "I should to sleep", "I will to try" — every single one sounds wrong with "to" added, and correct the moment it's removed: "I can swim", "I should sleep", "I will try", confirming this is a genuine rule for the whole modal category, not a one-off exception. His sister is right: modal verbs like "must" connect straight to the base verb with no "to" — "I must finish", not "I must to finish".