Differentiation of algebraic and trigonometric expressions can be used for calculating rates of change, stationary points and their nature, or the gradient and equation of a tangent to a curve.
From limits to integration, understanding the right method, not memorising formulas, is the real key to scoring higher in JEE Mathematics ...
Remember that integration is the inverse procedure to differentiation. So, if you can do trigonometric differentiation, you can do trig integration.