We consider extensions of General Relativity based on the non-local function <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msup><mrow><mo>□</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>R</mi><mo>)</mo></math>, where R is the Ricci curvature scalar and the non-locality is due to the term <math><msup><mrow><mo>□</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>R</mi></math>. We focus on cosmological minisuperspaces and select viable models by the Noether Symmetry Approach. Then we find viable exact solutions pointing out the role of non-locality in cosmology.