Now I can understand this, because if you really look at it, regional cooperation offers a wider "remit" if you will of how regionalism works. When states are cooperating in a regional sphere, people kind of get it you know; they understand what it entails to cooperate. The ideas of pooling resources; public goods; electricity, etc all kind of fall into place.
Conversely talk of integration, and the eyes kind of glaze over. Integration--far from being unsexy -- is also a bit of a mouthful: how and what are you integrating towards? And if it's a region, how are you integrating the region? All the images that the former explanation conjures kind of stops short when we talk of "regional integration."
Now inasmuch as both terms are valid and can be used interchangeably, there clearly is a difference that cannot be sneezed at. In my humble opinion, I foresee regional integration to be something more deep, more structural. The integration is kind of the engine that helps create a region that is well-integrated and harmonized, and where many member states are speaking with one voice.
On the other hand, "regional cooperation" seems superficial to me: it's like member states only cooperate, without doing it at the structural level. A quick search reveals no real definition of "regional cooperation". In fact, Google lists no less than 9,500,000 results, whereas on regional integration, we obtain 9,000,000 results.
Those results probably speak more of how more popular regional cooperation is than "integration".
On another level, there is the case of regional institutions and how regional groupings cooperate within them.
Let's just end with a definition from WIKIPEDIA on regional integration (interestingly, there is no such WIKIPEDIA piece on "regional cooperation"!):
Regional integration is a process in which states enter into a regional agreement in order to enhance regional cooperation through regional institutions and rules. The objectives of the agreement could range from economic to political, although it has generally become a political economy initiative where commercial purposes are the means to achieve broader socio-political and security objectives. It could be organized either on a supranational or an intergovernmental decision-making institutional order, or a combination of both.
If one remembers nothing at all (given that there are reputedly no less than eight requirements for regional integration systems), remember the first line:
Regional integration is a process in which states enter into a regional agreement in order to enhance regional cooperation through regional institutions and rules.