∫(from -∞ to ∞)85cos(πt)dt = 2∫(from 0 to ∞)85cos(πt)dt (by symmetry)
= 170limb→∞[∫(from 0 to b)cos(πt)dt]
= (170/π)limb→∞[sin(πb) - sin0]
= (170/π)(limb→∞sin(πb))
Since limb→∞sin(πb) does not exist (because sin(πb) oscillates between -1 and 1 forever), the given integral is DIVERGENT.