Compute \(\int_0^3 2x\,dx\).

Compute \(\int_1^2 (3x^2+1)\,dx\).

Compute \(\int_{-1}^{1} x^3\,dx\).

Compute \(\int_0^{\pi/2}\cos x\,dx\).

Compute \(\int_1^4 \sqrt{x}\,dx\).

Compute \(\int_1^e \frac{1}{x}\,dx\).

Compute \(\int_0^2 |x-1|\,dx\).

Compute \(\int_2^0 (x+1)\,dx\).

If \(\int_0^5 f(x)\,dx=12\) and \(\int_0^2 f(x)\,dx=7\), find \(\int_2^5 f(x)\,dx\).

Compute the signed area \(\int_{-2}^{2}(x^2-1)\,dx\).