Find \(\frac{d}{dx}\int_1^x (t^2+3)\,dt\).

Find \(\frac{d}{dx}\int_0^{x^2}\cos t\,dt\).

Compute \(\int_2^5 4x^3\,dx\) using the Fundamental Theorem of Calculus.

Let \(G(x)=\int_x^4 e^t\,dt\). Find \(G'(x)\).

Let \(H(x)=\int_{x}^{x^2}(1+t^3)\,dt\). Find \(H'(x)\).

Find \(\frac{d}{dx}\int_3^{\sin x}\sqrt{1+t^2}\,dt\).

If \(F(x)=\int_0^x f(t)\,dt\) and \(f(2)=7\), find \(F'(2)\).

Compute \(\int_0^1 (6x^2-2x)\,dx\) using an antiderivative.

Let \(A(x)=\int_2^x \frac{1}{1+t^2}\,dt\). Find the equation of the tangent line to \(A\) at \(x=2\).

Find \(\frac{d}{dx}\int_{1}^{3x+1}\ln t\,dt\), for \(x>0\).