Calculus: Early Transcendentals, Chapter 5, 5.4, Section 5.4, Problem 27

You need to evaluate the definite integral using the fundamental theorem of calculus, such that: int_a^b f(x)dx = F(b) - F(a)
int_0^pi (5e^x+ 3sin x)dx = int_0^pi 5e^x dx + int_0^pi 3sin x dx
int_0^pi (5e^x+ 3sin x)dx = (5e^x - 3cos x)|_0^pi
int_0^pi (5e^x+ 3sin x)dx =5e^pi - 3cos pi - 5e^0 + 3cos 0
int_0^pi (5e^x+ 3sin x)dx = 5e^pi - 3*(-1) - 5 + 3
int_0^pi (5e^x+ 3sin x)dx = 5e^pi + 1
Hence, evaluating the definite integral yields
int_0^pi (5e^x+ 3sin x)dx = 5e^pi + 1