Divide the interval into subintervals, create rectangles/trapezoids, calculate their areas, and sum them up.

Find the antiderivative of the function, evaluate it at the upper and lower limits, and subtract the values.

Integrate the rate of change function over the given interval.

Integrate the absolute value of the velocity function over the given interval.

Choose u, find du, rewrite the integral in terms of u, integrate, and substitute back to the original variable.

Use the initial condition given, substitute into the equation, and solve for C.

Choose u, find du, change the bounds, rewrite the integral in terms of u, integrate, and evaluate using the new bounds.

Use long division to rewrite the integral, then integrate term by term.

Rewrite the denominator by completing the square, then use u-substitution and inverse trig functions.

Choose u and dv, find du and v, and apply the formula: $\int u dv = uv - \int v du$.

The derivative of the integral of a function is the original function itself.

The definite integral of a function can be evaluated by finding the difference of its antiderivative at the upper and lower limits of integration.

Find where the graph is positive, which means above the x-axis.

Find where the slope of f(x) is positive because that would be a positive second derivative of f(x).

Look for slope changes in the graph of f(x).

Use the derivative graph, f(x), to find changes in sign of the first derivative.

Identify candidates for absolute maximum and absolute minimum for the integrally defined function.