Integrative therapy isn't a modality, it describes a blending of different modalities, so what it looks like will depend on which modalities your therapist is integrating.
It sounds like your therapist is largely person-centred and/or psychodynamic. Those modalities value the relationship and what emerges in it, which is why it is client led. I would recommend talking to your therapist about your therapy, what modalities s/he integrates, and how the work might be helpful to you. It's a collaborative endeavour and it's almost always helpful to discuss it with the therapist.