What is Newton Leibnitz formula with Examples ?

Newton Leibnitz formula If h(x) and g(x) are differentiable functions of x then, $$d\over dx$$ $$\int_{g(x)}^{h(x)}$$ f(t)dt = f[h(x)].h'(x) – f[g(x)].g'(x) Example : Evaluate $$d\over dt$$ $$\int_{t^2}^{t^3}$$ $$1\over log x$$ dx Solution : We have, $$d\over dt$$ $$\int_{t^2}^{t^3}$$ $$1\over log x$$ dx = $$1\over log t^3$$ $$d\over dt$$ $$(t^3)$$ – $$1\over log t^2$$ $$d\over dt$$ …