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JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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It is possible to make Custom PHP page which will post data from your form on that page. If you want to achieve that it will be good first to read this article. In few steps I will try to explain you how to do this.
1. Inside of JotForm builder select Thank You option
2. Choose Custom URL
3. Click on Next
4. Add URL of page of your site
5. On that page (step 4) you need to write PHP code which will collect all of data from your form. Inside of article mentioned above you will find more information about how to write custom PHP code.
6. Last step is to enable Send Post Data feature of the form.
Hope this will help.
@Laura, I see that the answer provided by @bkljaic is correct.
Please give it a try and let us know if you need further assistance.