https://notendur.hi.is/vae11/%C3%9Eekking/principles_of_mathematical_analysis_walter_rudin.pdf
(37) $\ \int_{\phi} cw =c\int_{\phi} w$
He says by (37),
(39)$\ \int_{\phi} (-w) =-\int_{\phi} dw$
How does property (39) Come about in page 256? I don't think he even defined the differential of a differential form.
To get this off the unanswered queue,
Answer by kimchi lover