If you fast the tenth and eleventh of Muharram with the intention of making up missed Ramadan fasting, that is permissible and will make up for two of the days that you owe.

Fasting on the day of 'Ashura or `Arafah only expiates minor sins; as for major sins, they require sincere repentance. But falling into major sin does not mean that you should refrain from doing acts of worship and good deeds.