Using integration to solve greatest contiguous sum problem

integration.coffee

integrate = (array) ->
  total = 0

  array.map (n) ->
    total += n

zeros = (array) ->
  array.reduce (zeros, n, i) ->
    if !(array[i-1] > 0) and n > 0
      zeros.push i
  , []

greatestContiguousSum = (array) ->
  Sarray = integrate(array)

  end = max(Sarray)
  start = zeros(Sarray).filter (zero) ->
    zero < end
  .last()