When creating a new Lead Capture form you can choose to send submissions directly to your HubSpot account.
Step 1 - Add A New Provider
Under the integrations tab select 'providers' and click the 'add a new provider button'
Step 2 - Connect To HubSpot
Enter your API Key as shown below.
Step 3 - Select Your List
When someone opts-in to your form their details will be added to a HubSpot list of your choice.
Please note that you can only add leads to static contact lists in HubSpot.