Bounding the Integral: If m <= f(x) <= M on [a,b], then m(b-a) <= integral(a,b) f(x)dx <= M(b-a).

Using Monotonicity: If f is increasing on [a,b]: f(a)(b-a) <= integral <= f(b)(b-a). If f is decreasing: f(b)(b-a) <= integral <= f(a)(b-a).

Comparison Method: To compare integral(0 to 1) e^(x^2) dx with integral(0 to 1) e^x dx: On [0,1]: x^2 <= x, so e^(x^2) <= e^x. Therefore integral(0,1) e^(x^2) dx <= integral(0,1) e^x dx = e-1.

JEE Application: These are used in assertion-reasoning and multiple-correct questions.