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.