Signed Area: integral(a,b) f(x)dx gives SIGNED area: positive above x-axis, negative below.

Total Area (unsigned): integral(a,b) |f(x)| dx. Must split at zeros of f(x).

Area Between Curves: integral(a,b) [f(x) - g(x)] dx where f(x) >= g(x) on [a,b].

Caution: If curves cross within [a,b], split at crossing points and take |f-g| in each sub-interval.

JEE Pattern: "Find the area bounded by y = f(x), y = g(x), x = a, x = b." Always sketch to identify which function is on top in each sub-interval.