DEFINITE INTEGRAL | INTRODUCTION OF DEFINITE INTEGRATION, EVALUATION OF DEFINITE INTEGRALS, DEFINITE INTEGRATION BY TYPICAL SUBSTITUTION, PROPERTIES OF DEFINITE INTEGRALS | Fundamental Theorem of Definite Integration, `int_a ^b f(x) dx = phi(b) - phi(a)`, Examples: `int_2 ^4 x / (x^2 + 1) dx`, Definite integration by substitution, Examples: `int_0 ^1 sin^-1 ((2x )/ (1 + x^2)) dx`, Property 1: Integration is independent of the change of variable. `int_a ^b f(x) dx = int_a ^b f(t) dt`, Property 2: If the limits of a definite integral are interchanged then its value changes. `int_a ^b f(x) dx = - int_b ^a f(x) dx`, Property 3: `int_a ^b f(x) dx = int_a ^c f(x)dx + int_c ^b f(x) dx`, Property 4: If `f(x)` is a continuous function on `[a,b]` then `int_a ^b f(x) dx = int_a ^b f(a+b-x) dx`