Which option of the build allows the check-in to happen only if build is successful?

Gated Check-in is a TFS build option that requires a successful build before allowing changes to be committed to the repository. When you queue a gated check-in, TFS shelves your changes, builds them, and only commits them if the build passes. This prevents broken code from entering the main branch. Incremental and continuous check-in are not TFS terms.