Step 1 :Let the first integer be \(x\), the second integer be \(x+1\), and the third integer be \(x+2\)
Step 2 :Set up an equation: \(x + (x+1) + (x+2) = 171\)
Step 3 :Simplify the equation: \(3x + 3 = 171\)
Step 4 :Solve for \(x\): \(x = 56\)
Step 5 :Find the three consecutive integers: \(56, 57, 58\)
Step 6 :\(\boxed{The\ three\ consecutive\ integers\ are\ 56,\ 57,\ and\ 58}\)