---
title: "C.GSR.5: Fundamental Theorem of Calculus (Georgia Mathematics standard)"
code: C.GSR.5
cite_as: Georgia Standards of Excellence, Mathematics, C.GSR.5
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/C.GSR.5
md_url: https://georgiahomeroom.org/standards/code/C.GSR.5.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/C.GSR.5.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# C.GSR.5: Fundamental Theorem of Calculus

Analyze the relationship between the derivative and the integral using the Fundamental Theorem of Calculus.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Evaluate and interpret definite integrals.
  - **C.GSR.5.1**: Use Riemann sums to approximate values of definite integrals.
  - **C.GSR.5.2**: Interpret a definite integral as a limit of Riemann sums.
  - **C.GSR.5.3**: Find the exact value of a definite integral using geometric formulas on a coordinate plane.
  - **C.GSR.5.4**: Demonstrate the use of properties of definite integrals.
  - **C.GSR.5.5**: Apply the Fundamental Theorem of Calculus as an interpretation of the accumulation in the rate of change of a function as equivalent to the change in the antiderivative over the interval.
- Find the antiderivative of indefinite integrals.
  - **C.GSR.5.6**: Apply Fundamental Theorem of Calculus to indefinite integrals to represent the family of antiderivatives.
  - **C.GSR.5.7**: Apply integration by substitution to definite and indefinite integrals.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.