If you want to mark them as read, tap "Edit" in Inbox. You'll find it at the top. At the bottom, "Mark All" will appear. Tap it, then select "Mark As Read".
If you want to remove them from the Inbox all at once, this has to be done with iOS 7 or 8 installed:
Again, tap "Edit". Check mark the first email. This time, tap "Move" at the bottom and hold it. While holding "Move", un-checkmark the first email again, then let go of the "Move" button. At the right, you'll see the emails from the account. At the left, you'll find the Mailboxes. Tap the mailbox where the emails should appear afterwards.