How to do integration testing with RSpec and Devise/CanCan?

@pschuegr’s own answer got me across the line. For completeness, this is what I did that gets me easily set up for both request specs and controller specs (using FactoryGirl for creating the user instance):

in /spec/support/sign_in_support.rb:

#module for helping controller specs
module ValidUserHelper
  def signed_in_as_a_valid_user
    @user ||= FactoryGirl.create :user
    sign_in @user # method from devise:TestHelpers
  end
end

# module for helping request specs
module ValidUserRequestHelper

  # for use in request specs
  def sign_in_as_a_valid_user
    @user ||= FactoryGirl.create :user
    post_via_redirect user_session_path, 'user[email]' => @user.email, 'user[password]' => @user.password
  end
end

RSpec.configure do |config|
  config.include ValidUserHelper, :type => :controller
  config.include ValidUserRequestHelper, :type => :request
end

Then in request spec:

describe "GET /things" do
  it "test access to things, works with a signed in user" do
    sign_in_as_a_valid_user
    get things_path
    response.status.should be(200)
  end
end

describe "GET /things" do
  it "test access to things, does not work without a signed in user" do
    get things_path
    response.status.should be(302) # redirect to sign in page
  end
end

and similarly, use ‘signed_in_as_valid_user’ in controller specs (which wraps Devise::TestHelpers sign_in method with a user from FactoryGirl)