We present a new implementation of validated arbitrary-precision numerical evaluation of definite integrals $\int_a^b f(x) dx$, available in the Arb library. The code uses a version of the Petras algorithm, which combines adaptive subdivision with Gauss-Legendre (GL) quadrature, evaluating the integrand on complex intervals surrounding the path of integration to obtain rigorous error bounds. The first part of the talk discusses the general algorithm and its performance for interesting families of integrals. The second part, which is based on joint work with Marc Mezzarobba, discusses the fast computation of GL quadrature nodes with rigorous error bounds. It is well known that GL quadrature achieves a nearly optimal rate of convergence for analytic integrands with singularities well isolated from the path of integration, but due to the cost of generating GL quadrature nodes, the more slowly converging Clenshaw-Curtis and double exponential quadrature rules have often been favored when an accuracy of several hundreds or thousands of digits is required. We consider the asymptotic and practical aspects of this problem. An order-of-magnitude speedup is obtained over previous code for computing GL nodes with simultaneous high degree and precision, which makes GL quadrature viable even at very high precision.