i am finding difficulty in integration and differentiation of the greatest integer function [x],especially with limits.kindly help me in understanding it in dept.

If this were the integral from 0 to x, where x is less then 1, it would be x.
If this were the integral from 0 to x, where x is between 1 and 2, it would be 1+2x.
If this were the integral from 0 to x, where x is between 2 and 3, it would be 3+3x.
If this were the integral from 0 to x, where x is between 3 and 4, is would be 6+4x.

Having done these, if this were the integral from 0 to x where x is between n and n+1,
the answer would be sum(1:n) + (n+1)x.
That is, n(n+1)/2 + (n+1)x.  


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