Euler E651: Four particularly noteworthy theorems in integral calculus | English translation | OMH v1.0

English translation of Leonhard Euler's E651, Four particularly noteworthy theorems in integral calculus. AI use and review status: OpenAI tools assisted with the translation and LaTeX. Version 1.0 is a machine draft with limited scholarly human inspection. Version 2.0 is reserved for a fully reviewed edition. Sources: Euler Archive, E651, https://scholarlycommons.pacific.edu/euler-works/651/ ; Nova Acta Academiae Scientiarum Imperialis Petropolitanae, VII (Academy history through 1789; printed 1793), pp. 22–41, https://archive.org/details/novaactaacademia07impe ; American Museum of Natural History Library / Biodiversity Heritage Library, item 38589, https://www.biodiversitylibrary.org/item/38589 .