As you have asked about the act under which Municipal Corporation in India was formed, I am giving you information about it, check below for the details

They are formed under the Corporations Act of 1835 of Panchayati Raj system which mainly deals in providing essential services in Metropolitan Cities.

The no. of councillors depend upon the area and population of the city that minimum of 3,00,000.
Municipal Corporation members are elected from the several wards of the specific city on the basis of adult franchise for a term of five years.
There are seats reserved for Scheduled Castes, Scheduled Tribes, backward classes and women.
The Councillors are chosen by direct election from electoral wards in the Municipal Corporation.

Municipal Corporations are urban local government that works for the development of a city, which has a population of more than one million (ten lakh).

Functions
Municipal Corporation building in Bangalore

Water supply
Hospitals
Roads
Over bridge
Street lighting
Drainage
Solid waste
Fire brigades
Market places
Records of births and deaths

It also helps in education and primary health care