This occurs when the integrand is continuous on the relevant interval. Under this condition, the Fundamental Theorem of Calculus states that the derivative of the integral with respect to its upper limit is the integrand evaluated at that limit.
Conditions: The integrand is continuous on the interval of integration.; The upper endpoint is the variable with respect to which we are differentiating (before applying the chain rule for a composite limit).
This occurs when the integrand is continuous on the relevant interval. Under this condition, the Fundamental Theorem of Calculus states that the derivative of the integral with respect to its upper limit is the integrand evaluated at that limit.
Conditions: The integrand is continuous on the interval of integration.; The upper endpoint is the variable with respect to which we are differentiating (before applying the chain rule for a composite limit).