The range, usually of a function, is the set of value that the function can take. The integral range is a subset of the range consisting of integer values that the function can take.
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Particular integral is finding what the integral is for example the integral of 2x is x^2 + C. Finding the particular solution would be finding what C equals from the particular integral.
In simple language, derivative is rate of change of something and integral represents the area of a curve whose equation is known.
The range is the spread between maximum and minimum values.
Range is the difference between the largest and smallest numbers