Real Dictionary

integral in American English
necessary for completeness; essential
adjective: of, pertaining to, or belonging as a part of the whole; constituent or component
noun: an integral whole

integral in British English
adjective: being an essential part (of); intrinsic (to)
noun: the limit of an increasingly large number of increasingly smaller quantities, related to the function that is being integrated (the integrand). The independent variables may be confined within certain limits ( definite integral) or in the absence of limit

integral in Mechanical Engineering
adjective: An integral control is a type of control where the strength of the output is adjusted according to all the differences from the setpoint that have been recorded since the beginning of a process.