When the integrand involves some trigonometric functions, we use some well-known identities to find the integrals. Using the substitution technique, we obtain the following standard integrals.

Remember that integration is the inverse procedure to differentiation. So, if you can do trigonometric differentiation, you can do trig integration.

Zygmund's “Trigonometric Series” in 1935, there has been considerable demand for another book dealing with trigonometric integrals ... book on the theory of functions, and his new book ...