How to write an integration test for a function with RestSharp Response using Nsubstitute and Xunit

I am not familiar with the integration tests. How can I write an Integration test for the following code? is the Integration test similar to the Unit test? Is it possible to Mock RestClient in Nsubstitute.

public class AttachProviderService : IAttachProviderService
{
    private readonly ILogger<AttachProviderService> _logger;
    private readonly string AdminRead;
    private readonly RestClient adminReadClient;
    private readonly int _apiTimeout;
    public AttachProviderService(IConfiguration configuration, ILogger<AttachProviderService> logger)
    {
        _logger = logger;
        this.AdminMgmtReadAPI = $"{configuration["AdminRead"]}api/SearchRead/";
        this.adminReadClient = new RestClient(AdminRead);
        this._apiTimeout = Convert.ToInt32(configuration["Timeout"]);
    }     

    public async Task<List<AttachProviderSearchResultViewModel>> GetAttachProviderSearchList(AttachProviderSearchViewModel attachProviderSearch)
    {
        RestResponse<List<AttachProviderSearchResultViewModel>> response;
        try
        {
            _logger.LogInformation($"AttachProviderService/GetAttachProviderSearchList start");
            var request = new RestRequest(AdminReadAPIConstants.GetAttachProviderSearchList, Method.Post);
            request.Timeout = _apiTimeout;
            request.AddJsonBody(attachProviderSearch);
            response = await adminReadClient.ExecuteAsync<List<AttachProviderSearchResultViewModel>>(request);
            _logger.LogInformation($"AttachProviderService/GetAttachProviderSearchList end");
        }
       
        catch (Exception ex)
        {
            _logger.LogInformation($"AttachProviderService/GetAttachProviderSearchList end");
            throw ex;
        }
        return response.Data;
    }

}