In the following sentence, is the construction know + to + infinitive grammatical?
They want to eat food they know to be good for them.
The dictionary says that "know to do something" is a correct construction. But can it be used in the above example?
If correct, is the meaning of the sentence similar/identical to "They want to eat food they know is good for them"? If not, what's the difference? If yes, how do they sound to a native speaker? To me as a non-native speaker, the "...know is good..." one sounds OK, but the "...know to be good..." one is sort of clumsy.