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Verified Answer :

assume the first integer is \(x\).
then we have the sequence for the 6 numbers: 
\(x,x+1,x+2,x+3,x+4,x+5\)
their sum equals 519. so we have the equation
\((x)+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=519\)
now solve it. \(6x+15=519\)
\(6x=504\)
\(x=84\)
now that we know the value of \(x\), we can find the sequence of the integers:
\(84,85,86,87,88,89\)