Q.Evaluate $\displaystyle\int_{0}^{3} (x^{2}+1)\,dx$ using the Fundamental Theorem of Integral Calculus.

Find one antiderivative, then apply the Fundamental Theorem by evaluating it at the upper limit and subtracting its value at the lower limit.

Find an antiderivative of $f(x)=x^{2}+1$ using formula 1:

Evaluate at the limits:

Apply the Fundamental Theorem: …

Forgetting the constant term $+1$ when finding the antiderivative, integrating only $x^{2}$ to get $\frac{x^{3}}{3}$ and dropping the $+x$ term entirely — every term of the …