An integral approach also means to explore and apply tools from western and easter cultures, with their complementary yang (external focus) and yin (internal focus) approaches to existence.
Western culture has evolved a wide variety of tools that helps us predict (science) and manipulate (engineering etc) the physical aspect of existence. Eastern culture has evolved an equally impressive range of tools for exploring, understanding and working with the inner/experiential aspects of existence. And they all work, if chosen and applied with some skill.
Eastern traditions have evolved tools that help us explore the nature of mind and existence, to work with the energetic aspect of our being, to relate to inner and outer situations in a way that fuels compassion, wisdom, humility and gratitude.
If western culture takes their scientific approach seriously, there may be only a question of time before some of these tools are taught as a basic part of the education of all of us. Of course, there has to be some understanding of (a) the imporance of intention, (b) when and how to learn and apply each tool, and (c) the context within which to apply them. As with any tools, they can be used to open us up or for contraction.