Usually an integral is applied to a continuous function (eg temperature) while summations are applied to discrete functions (eg. car manufacture or crowd capacity?)
They both represent 'the area under the curve' in some sense.
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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.
there is no diffference, i think...
In simple language, derivative is rate of change of something and integral represents the area of a curve whose equation is known.
Both kinds of integrals are essentially calculations of areas under curves. In a definite integral the surface whose area is to be calculated is planar. In a line integral the surface whose area to be calculated might occupy two or more dimensions. You might be interested in the animated diagrams in the wikipedia article for the line integral.