The document discusses integrating a function f that is continuous and greater than or equal to 0 on the real numbers. It states that to justify this with a diagram, one can make a substitution of x=t+c in the integral, so that dx=dt and the limits of integration change from a+c to b+c, or a to b. This allows the integral to be written as the integral of f(t+c) from a to b, with the integration variable replaced from t to x.

1. justify with appropriate diagram. Assume f is continuous on R and f is greater than equal to zero
for diagram
Solution
putting x=t+c in the problem dx=dt therefore now we have to integrate f(t+c) from
t+c=a+c to t+c=b+c or from a to b the problem becomes the integral of f(t+c) from a to b in
integration variable can be replaced from t to x