Integrals

Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
$\int \frac{d x}{x^2 \pm a^2}$, $\int \frac{d x}{\sqrt{x^2 \pm a^2}}$, $\int \frac{d x}{\sqrt{a^2-x^2}}$, $\int \frac{d x}{a x^2+b x+c}$, $\int \frac{d x}{\sqrt{a x^2+b x+c}}$, $\int \frac{p x+q}{a x^2+b x+c} dx$, $\int \frac{p x+q}{\sqrt{a x^2+b x+c}} dx$, $\int \sqrt{a^2 \pm x^2} d x$, $\int \sqrt{x^2-a^2} dx$, $\int \sqrt{a x^2+b x+c} d x$
Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.