How to use this calculator
A signed integral counts area above the x-axis positively and area below it negatively. Total geometric area adds both magnitudes. For a polynomial, this tool builds an antiderivative term by term; total-area mode splits the interval at real zeros before summing absolute contributions.
The method
Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.
Polynomial coefficients: 1, 0, -1 Lower bound a: -2 Upper bound b: 2 Area convention: Signed definite integral
Signed definite integral: 1.3333333333
Between x = -2 and x = 2.
Scope and limitations
Continuous polynomials of degree 6 or less. Arbitrary functions, discontinuities, and infinite bounds are not supported. Polynomial integration is analytic, while root locations and evaluations use finite numerical precision.
Common questions
Can a signed integral be negative?
Yes. If the negative contributions dominate, the signed integral is negative even though geometric area is nonnegative.
Why can total area be larger than the absolute signed integral?
Positive and negative pieces cancel in a signed integral but are both added in total-area mode.
References & further reading
External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.