You can simplify your code a lot by using the initializer list.
DisplayManager::DisplayManager(int screenWidth, int screenHeight)
: screenWidth(screenWidth)
, screenHeight(screenHeight)
, mainWindow(sf::VideoMode(screenWidth, screenHeight, 32), "FooBar")
{
// constructor body is empty
}
Do you even need to store the width and height? Recall that sf::RenderWindow has two methods GetWidth() and GetHeight(). Then you could just do it like this:
DisplayManager::DisplayManager(int screenWidth, int screenHeight)
: mainWindow(sf::VideoMode(screenWidth, screenHeight, 32), "FooBar")
{
}