You can't check this with minitest
alone.
You should be looking at Capybara to achieve this.
Capybara helps you test web applications by simulating how a real user would interact with your app.
Once setup use has_title? matcher to test the title of the rendered page.
Using Capybara you can test various aspects of your page like its content/text, if it has a particular link or not, a particular button, text field, email field, etc. You can simulate the behavior of filling up a form and clicking on a button to submit the same. Putting it simply, it just behaves as a real user would by simulating the actions that a user can perform on a given page with what all a user can see on a given page.